Current Advances in High-Dimensional Estimation in Survey Sampling: Challenges, Solutions, and Future Priorities
1. Introduction: The New Frontier of High-Dimensionality in Survey Sampling
The field of survey sampling is undergoing a significant transformation, driven by the increasing availability and complexity of data. A central aspect of this evolution is the challenge and opportunity presented by high-dimensional estimation. Traditionally, survey data analysis operated in settings where the number of auxiliary variables or features, denoted by p, was considerably smaller than the sample size, n.1 High-dimensional estimation in the survey context, however, refers to scenarios where p is large, potentially exceeding or being comparable to n.2 This is not merely a matter of "big data" in terms of sample volume, but rather the intricate complexity introduced by a vast number of potential predictors or auxiliary variables available for each sampled unit. This shift fundamentally challenges the classical survey sampling paradigm, which was largely developed under the assumption of a limited set of well-chosen auxiliary variables. The advent of modern data collection capabilities, including administrative records, sensor data, and digital footprints, provides an unprecedented wealth of auxiliary information.4 National Statistical Offices (NSOs) and other statistical organizations are increasingly encountering and seeking to leverage such data to enhance the precision of survey estimates, such as population totals and means.5
The drive to utilize high-dimensional auxiliary data stems from the promise of substantially improved estimator efficiency and the potential to address more complex analytical objectives, such as small area estimation and more nuanced nonresponse adjustments. However, this potential is intrinsically linked with considerable methodological risks if not managed appropriately. Incorporating an excessive number of auxiliary variables into estimation procedures can paradoxically lead to a loss of efficiency or the introduction of additional variability.4 This report provides a comprehensive overview of the current landscape of high-dimensional estimation in survey sampling. It will delve into the fundamental challenges posed by high-dimensionality, explore the array of methodological advances and solutions developed to address these issues, and outline key priorities for future research in this rapidly evolving domain.
2. Fundamental Challenges in High-Dimensional Survey Estimation
The application of estimation techniques to survey data characterized by a large number of variables relative to the sample size introduces a host of complex challenges. These difficulties span statistical theory, computational feasibility, and the practicalities of complex survey designs.
2.1 The "Curse of Dimensionality" in Surveys
The "curse of dimensionality" refers to a collection of phenomena that arise when analyzing data in high-dimensional spaces.
●	Overfitting and Noise Accumulation: A primary concern is overfitting, where models with an excessive number of variables tend to capture random noise in the sample rather than the true underlying relationships in the population. This leads to poor generalization to new data and unstable estimates.2 In the survey context, this implies that auxiliary variables might reflect spurious correlations present only in the specific sample, not in the broader population. The accumulation of noise from many irrelevant or weakly relevant predictors can obscure true signals.8 Penalized least squares approaches, often used to manage high dimensionality, can themselves lose efficiency if the data contain outliers or exhibit heteroscedasticity, issues that are often exacerbated in high-dimensional spaces.9
●	Multicollinearity: With a large p, the likelihood of high correlations among auxiliary variables increases significantly. Multicollinearity makes it difficult to disentangle the individual contributions of these variables, leading to unstable and unreliable coefficient estimates in model-assisted approaches.2 This instability means that small changes in the data or model specification can lead to wildly different coefficient estimates.11
●	Singular Covariance Matrices: When the number of variables p exceeds the sample size n, the sample covariance matrix of the auxiliary variables can become singular (i.e., non-invertible). This poses a significant problem for many multivariate statistical techniques that rely on the inverse of this matrix.2
●	Increased Sparsity of Data: As the number of dimensions increases, the volume of the feature space grows exponentially. Consequently, the available data points become increasingly sparse within this expanded space, making statistical approximations and density estimations less reliable.8
These challenges are often interconnected, creating a cascade effect. For instance, high dimensionality frequently leads to multicollinearity. If all these correlated variables are used in a model-assisted estimator like the Generalized Regression (GREG) estimator, the underlying model coefficients can become unstable. This instability, in turn, compromises the quality of predictions used in the GREG estimator, making the final survey estimate unreliable. Subsequently, attempting to estimate the variance of this already problematic GREG estimator becomes even more difficult, as standard variance estimation techniques themselves are biased in high-dimensional settings.10
Furthermore, the "curse of dimensionality" is not solely about the condition p>n. Even when p<n, if a large proportion of the auxiliary variables are noisy or irrelevant to the survey variables of interest, the effective dimensionality can still pose substantial problems. This leads to "noise accumulation," where the influence of many uninformative predictors can overwhelm the signal from the few truly relevant ones.8 This implies that variable selection and regularization techniques are crucial not only when p is very large but also when p is moderately large and the quality of auxiliary information is mixed.
2.2 Computational Complexity and Scalability
Algorithms developed for traditional low-dimensional survey data often face prohibitive computational burdens when applied to high-dimensional settings. Operations such as matrix inversion, eigen-decomposition, and exhaustive search strategies for model selection scale poorly with increasing p.2 This necessitates the development of computationally efficient algorithms capable of handling both large p and potentially large n, which are characteristic of modern survey datasets combined with auxiliary data sources.14 Classical statistical inference methods are often not directly applicable, highlighting the need for computational and methodological advances.3
2.3 Instability and Bias in Traditional Survey Estimators
The influx of high-dimensional auxiliary information can adversely affect standard survey estimators if not handled appropriately.
●	Calibration Estimators: Calibration is a widely used technique in survey sampling to ensure consistency with known population totals of auxiliary variables and to potentially reduce variance. However, incorporating an excessive number of auxiliary variables in calibration estimators—a phenomenon sometimes termed "over-calibration"—can lead to increased variance of the resulting estimates and may even introduce bias if the underlying implicit model is misspecified.4 The weights derived from such over-calibration can also exhibit undesirable properties, such as high variability.
●	Variance Estimators: A significant challenge in high-dimensional survey estimation is the performance of customary variance estimators. Methods such as Taylor linearization and jackknife replication, which are mainstays in survey practice, can suffer from substantial bias when p is large relative to n.1 Theoretical and empirical investigations show that Taylor-based methods may underestimate the true variance, while jackknife-based methods may lead to overestimation.1 This bias can invalidate confidence intervals and hypothesis tests, undermining the reliability of survey inferences.
2.4 Issues with Complex Survey Designs in High-Dimensional Contexts
The unique features of complex survey designs, such as weighting, stratification, and clustering, introduce additional layers of complexity when dealing with high-dimensional data.
●	Weighting: Survey weights are essential for producing unbiased or consistent estimates from samples selected with unequal probabilities and for adjusting for nonresponse. However, the interaction between survey weights and high-dimensional modeling is intricate. Standard statistical software, particularly for machine learning algorithms, may not adequately handle survey weights or may do so in a way that is not theoretically justified for design-based inference.20 The construction of survey weights itself, often involving post-stratification, becomes more challenging with a high number of potential auxiliary variables, as the number of post-stratification cells can explode, leading to unstable weights or cells with very few or no sample units.20
●	Stratification and Clustering: These design features are implemented to improve efficiency (stratification) or reduce costs (clustering), but they inherently affect the variance structure of survey estimates and the effective sample size. Their impact must be correctly accounted for in any high-dimensional modeling or estimation procedure to ensure valid inferences.22
●	Incorporating Design Features into Modern Methods: A pivotal challenge is the adaptation of modern statistical techniques, such as penalized regression and machine learning algorithms, which are often developed under the assumption of independent and identically distributed (i.i.d.) data, to correctly incorporate complex survey design features.23 The traditional survey sampling principle of "conditioning on all design variables" 20 for model-based inference becomes practically infeasible or statistically unstable in high-dimensional settings. If, for instance, design variables include numerous detailed geographic indicators or fine-grained stratification variables, incorporating all of them into a model could lead to extreme multicollinearity or an unmanageably large number of parameters or post-stratification cells. This necessitates a re-evaluation of how to achieve design-respectful inference, pushing the field towards methods like regularization that can implicitly handle many variables or select relevant ones, or towards more sophisticated weighting adjustments.
2.5 Handling Missing Data in High-Dimensional Survey Settings
High-dimensional datasets are often accompanied by an increased likelihood of missing data, either in the auxiliary variables themselves or in the survey outcome variables.24 Traditional imputation methods may struggle when the number of predictors available for imputation is very large, potentially leading to biased or inefficient imputations. The interplay between missing data mechanisms (Missing Completely At Random - MCAR, Missing At Random - MAR, Missing Not At Random - MNAR), the chosen imputation methods, and subsequent high-dimensional estimation procedures requires careful consideration, especially under complex survey designs where weights and design features also play a role in the nonresponse process or its adjustment.24
The following table summarizes the key challenges discussed:
Table 1: Summary of Key Challenges in High-Dimensional Survey Estimation

Challenge Category	Description	Key Implications for Survey Practice	Illustrative References	
Curse of Dimensionality	Difficulties arising from a large number of variables (p) relative to sample size (n).			
\hspace{5mm} Overfitting & Noise Accumulation	Models capture sample noise rather than true population signals; irrelevant variables obscure true effects.	Unreliable estimates, poor predictive performance, incorrect variable importance.	2	
\hspace{5mm} Multicollinearity	High correlation among auxiliary variables.	Unstable coefficient estimates in models, difficulty in interpreting individual variable effects.	8	
\hspace{5mm} Singular Covariance Matrices	Sample covariance matrix of auxiliary variables becomes non-invertible when p>n.	Inability to use standard multivariate methods relying on matrix inversion.	2	
\hspace{5mm} Increased Data Sparsity	Data points become isolated in high-dimensional space.	Reduced reliability of statistical approximations and density estimates.	8	
Computational Complexity	Algorithms designed for low-dimensions become prohibitively slow or infeasible.	Need for scalable algorithms, limits on the complexity of models that can be practically implemented.	2	
Instability/Bias in Traditional Estimators				
\hspace{5mm} Calibration Estimators	"Over-calibration" with too many auxiliary variables leads to increased variance or bias.	Loss of efficiency, unstable survey weights.	4	
\hspace{5mm} Variance Estimators	Standard methods (Taylor, Jackknife) suffer substantial bias (underestimation or overestimation).	Invalid confidence intervals and hypothesis tests, unreliable measures of precision.	1	
Complex Survey Design Interactions	Difficulty in appropriately accounting for survey weights, stratification, and clustering in high-dimensional models.	Biased estimates if design is ignored, challenges in adapting i.i.d.-based methods (e.g., ML) to survey data.	20	
Missing Data	Increased likelihood of missing values in high-D settings; traditional imputation methods may struggle.	Biased or inefficient estimates if missing data are not handled properly, complex interactions with survey design and estimation.	24	
3. Methodological Advances and Solutions for High-Dimensional Data
In response to the challenges posed by high-dimensional auxiliary information in survey sampling, researchers have developed and adapted a range of statistical methods. These approaches aim to harness the potential benefits of rich auxiliary data while mitigating the risks of overfitting, instability, and computational burden. The choice among these methods often depends on the specific data characteristics, such as the degree of sparsity or multicollinearity, the ratio of p to n, and the primary analytical objective, be it prediction, parameter estimation, or causal inference. There is no single "silver bullet"; rather, a toolkit of techniques is emerging. Many of these solutions involve inherent trade-offs, for example, between bias and variance, or between computational feasibility and statistical optimality. For instance, penalized regression methods intentionally introduce some bias in coefficient estimates to achieve a larger reduction in variance.26 Similarly, dimension reduction techniques like Principal Component Analysis (PCA) can lead to loss of information or reduced interpretability of the transformed variables.2 A common practical strategy, particularly for ultra-high dimensional problems where p vastly exceeds n, involves a multi-stage approach: an initial screening or dimension reduction phase to reduce the number of variables to a more manageable set, followed by more refined modeling or selection techniques.27
The following table provides an overview of the main classes of methodological solutions:
Table 2: Overview of Methodological Approaches for High-Dimensional Survey Estimation

Method Category	Specific Techniques	Primary Application in Surveys	Key Advantages	Noted Limitations/Challenges	Illustrative References	
Adapted Model-Assisted/ Calibration Estimators	Ridge-penalized calibration, Principal Component Regression (PCR)-based calibration, Variable selection before calibration	Improving efficiency of population total/mean estimators, ensuring consistency with known totals	Reduces variance from over-calibration, handles multicollinearity	Choice of penalty/components, potential loss of interpretability with PCA, selection bias.	4	
Penalized Regression	Lasso, Ridge, Elastic Net, SCAD, MCP	Variable selection, model-assisted estimation, imputation, propensity score estimation	Simultaneous variable selection & estimation, handles multicollinearity, can achieve sparsity	Introduces bias, choice of tuning parameter, post-selection inference can be complex.	2	
Dimension Reduction	Principal Component Analysis (PCA), Partial Least Squares (PLS), Sure Independent Screening (SIS), Rough Feature Selection (RFS)	Reducing number of auxiliary variables before modeling or calibration, feature engineering	Simplifies models, reduces noise, SIS effective for ultra-high dimensions	PCA lacks interpretability, SIS is a screening tool, potential information loss.	2	
Model Selection Strategies	Risk Inflation Criterion corrected (RICc), Least Angle Regression with RICc (LAR-RICc)	Selecting optimal subset of auxiliary variables for models or calibration	RICc designed for consistency in high-dimensions, LAR-RICc computationally feasible	Performance depends on initial model sequence (LAR), exhaustive search still hard for large p.	28	
3.1 Adapting Model-Assisted and Calibration Estimators
Model-assisted estimators (such as the GREG estimator) and calibration estimators are foundational tools in survey sampling, designed to enhance the efficiency of Horvitz-Thompson estimators by leveraging auxiliary information.4 The primary challenge lies in their application when the available auxiliary data are high-dimensional. Direct application with an excessive number of auxiliary variables can paradoxically lead to increased variance, a phenomenon known as "over-calibration," and may not yield the anticipated efficiency gains.4
Several strategies have been proposed to improve the efficiency of these estimators in high-dimensional settings:
●	Ridge-type Penalization: Incorporating a ridge penalty (L2 penalization) during the model-fitting stage of model-assisted estimation, or directly into the calibration weighting procedure, can stabilize the estimates. This is particularly effective when the auxiliary variables are numerous and exhibit multicollinearity. The ridge penalty shrinks the regression coefficients associated with the auxiliary variables, thereby reducing the variance of the final survey estimates.4
●	Dimension Reduction via Principal Component Regression (PCR): An alternative approach involves performing PCA on the high-dimensional set of auxiliary variables and then using a subset of the resulting principal components (which are uncorrelated linear combinations of the original variables) as regressors in a model-assisted framework or as variables for calibration.2 This reduces the dimensionality of the problem while aiming to retain most of the explanatory power of the auxiliary information.
●	Variable Selection Prior to Calibration: Instead of using all available auxiliary variables, a preliminary step of variable selection can be employed to identify a smaller, more relevant subset. These selected variables are then used in the calibration process. Techniques such as bootstrap-based criteria have been suggested to guide this selection, aiming to achieve a more parsimonious set of calibration variables, which can lead to weights with smaller variation and avoid variance inflation.18 Comparative studies have shown that while the traditional GREG estimator performs poorly as the number of auxiliary variables increases, model-assisted estimators based on penalized methods (like Ridge and Lasso) or tree-based models (like Random Forests) can exhibit greater robustness and efficiency.17
3.2 Penalized Regression Methods
Penalized regression methods, such as Lasso (Least Absolute Shrinkage and Selection Operator), Ridge Regression, and Elastic Net, have become central to high-dimensional statistical modeling. These methods modify the standard estimation objective function (e.g., minimizing sum of squared errors) by adding a penalty term that depends on the size of the regression coefficients.2 This penalty encourages simpler models by shrinking some or all coefficients towards zero.
●	Lasso (L1 penalty): The Lasso penalty is proportional to the sum of the absolute values of the coefficients (∣∣β∣∣1​). Its key property is that it can shrink some coefficients to exactly zero, effectively performing variable selection by excluding irrelevant predictors from the model.2
●	Ridge Regression (L2 penalty): The Ridge penalty is proportional to the sum of the squared values of the coefficients (∣∣β∣∣22​). It shrinks all coefficients towards zero but does not typically set them exactly to zero. Ridge regression is particularly useful for handling multicollinearity, as it stabilizes coefficient estimates when predictors are highly correlated.2
●	Elastic Net: This method combines L1 and L2 penalties, offering a compromise between Lasso and Ridge. It can select groups of correlated variables and tends to be more stable than Lasso when p>n or when there is high multicollinearity.2
●	Other Penalties (e.g., SCAD, MCP): Non-convex penalties like the Smoothly Clipped Absolute Deviation (SCAD) and Minimax Concave Penalty (MCP) have been developed to mitigate some of the limitations of Lasso, such as its tendency to over-shrink large coefficients. Under certain conditions, these penalties can lead to estimators with "oracle properties," meaning they perform as well as if the true underlying model were known in advance.25
In the context of survey sampling, penalized regression methods are applied in various ways: in the modeling step of model-assisted estimation to select relevant auxiliary variables and estimate their effects, for imputing missing data when many predictors are available, or for estimating propensity scores for nonresponse adjustment in high-dimensional covariate spaces.7
A critical consideration with penalized estimators, particularly Lasso, is that the shrinkage process can introduce bias into the estimated coefficients of the truly important variables.26 While this bias helps reduce overall mean squared error, it can be problematic if accurate estimation of specific coefficients or valid confidence intervals are required. Consequently, research has focused on post-selection inference techniques, including debiased estimators and methods for constructing valid confidence intervals after variable selection.26 Weighted Lasso approaches, where different penalties are applied to different coefficients based on initial estimates or other information, have also been explored.33
3.3 Dimension Reduction Techniques
Dimension reduction techniques aim to transform or select features to obtain a lower-dimensional representation of the data while preserving essential information.
●	Principal Component Analysis (PCA): PCA is an unsupervised method that transforms the original set of (potentially correlated) auxiliary variables into a new set of uncorrelated variables called principal components. These components are ordered such that the first few capture the largest proportion of the variance in the original data.2 A subset of these principal components can then be used in subsequent modeling or calibration procedures. While effective in reducing dimensionality, the principal components themselves can sometimes be difficult to interpret in terms of the original variables, and PCA is sensitive to the scaling of the original variables.2
●	Partial Least Squares (PLS): Unlike PCA, PLS is a supervised dimension reduction technique. It seeks to find a set of latent variables (similar to principal components) that maximize the covariance between the predictor variables and the response variable(s) of interest.2 This makes it particularly useful when the goal is prediction.
●	Feature Selection Methods: These methods aim to identify and retain only the most relevant subset of the original features for the task at hand. They can be broadly categorized 2:
○	Filter methods: Evaluate features based on their intrinsic properties (e.g., correlation with the outcome, variance) independently of the chosen model.
○	Wrapper methods: Use a specific predictive model to evaluate different subsets of features, selecting the subset that yields the best model performance.
○	Embedded methods: Perform feature selection as an integral part of the model training process. Penalized regression methods like Lasso are examples of embedded methods.
●	Sure Independent Screening (SIS): For ultra-high dimensional settings, where p can be orders of magnitude larger than n (e.g., in genomics or some modern administrative datasets), SIS provides a computationally efficient approach to drastically reduce dimensionality.27 SIS ranks features based on their marginal utility (e.g., marginal correlation with the response variable) and selects a subset of top-ranking features for further analysis. Iterative versions (iSIS) can improve performance. SIS has been shown to possess the "sure screening property," meaning that with high probability, it retains all the truly important variables, provided certain conditions are met. It can also lead to model selection consistency and has been adapted for longitudinal data.27
●	Rough Feature Selection (RFS): This approach, based on rough set theory, offers another avenue for feature selection in high-dimensional data by evaluating the indispensability of features.29
3.4 Model Selection Strategies
When faced with a high-dimensional set of potential auxiliary variables, selecting the "best" subset of these variables to include in a statistical model or calibration procedure is a critical and computationally challenging task.
Traditional model selection criteria like the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) may not perform well or yield consistent model selection in high-dimensional settings, especially when p>n.28
●	Risk Inflation Criterion corrected (RICc): The RICc has been proposed as a model selection criterion specifically for high-dimensional data.28 It is an extension of the Risk Inflation Criterion (RIC) with an additional correction term (2loglogpn​∣M∣σ2). RICc is designed to be consistent, meaning the probability of selecting the true underlying model (if it is among the candidates) converges to one as the number of potential predictors pn​ grows. Simulations have shown RICc to be more stable and to outperform AIC and BIC in high-dimensional, low sample size scenarios.28
●	LAR-RICc: Exhaustively searching all possible models to minimize RICc is computationally infeasible when pn​ is even moderately large. The LAR-RICc method combines the computational efficiency of Least Angle Regression (LAR) with the RICc criterion.28 LAR generates a sequence of candidate models by adding variables one at a time. RICc is then used to select the best model from this sequence. LAR-RICc can achieve consistent model selection if the true model is included in the sequence generated by LAR.
●	Three-step Procedure: Based on the properties of LAR-RICc, a practical three-step procedure for model selection in high-dimensional settings has been suggested: (1) Use LAR-RICc to remove redundant variables and significantly reduce the model space. (2) Perform an exhaustive subset selection using RICc on the reduced set of variables. (3) Estimate the parameters of the final selected model using ordinary least squares.28 This approach has shown promising results in real-data applications.
●	Selective Labeling Models: In specific contexts, such as simultaneous equation models where observed outcomes are conditional on prior choices (e.g., sample selection problems), specialized estimation procedures are needed for high-dimensional covariates. Research in this area addresses challenges like non-concavity of likelihood functions and the large number of covariates in each equation.36
4. Addressing Variance Estimation Challenges in High-Dimensional Surveys
Accurate variance estimation is fundamental for making valid statistical inferences from survey data, as it provides measures of precision for point estimates and is crucial for constructing confidence intervals and conducting hypothesis tests. As highlighted earlier, customary variance estimators, such as those based on Taylor linearization or jackknife replication, often exhibit substantial bias in high-dimensional settings where the number of auxiliary variables p is large relative to the sample size n.1 Specifically, Taylor expansion methods tend to underestimate the true variance, while jackknife methods may overestimate it. This breakdown is not a minor issue; it signifies that the asymptotic assumptions underpinning these classical methods no longer hold when p is large. The way residuals behave and how resampling techniques capture variability fundamentally changes in high-dimensional spaces. This necessitates a shift towards new or significantly adjusted approaches for variance estimation.
The failure of standard estimators often arises because the distribution of sample residuals in a high-dimensional regression (often an implicit part of model-assisted or calibration estimation) is not a good approximation of the true error distribution. For instance, the variance of sample residuals can be considerably smaller than the true error variance when p/n is large, leading to the underestimation observed in Taylor-linearized variance estimators.1 Conversely, the residuals involved in jackknife calculations can have a variance larger than the true error variance, contributing to overestimation.1
Effective variance estimation in high dimensions often requires a more integrated approach with the point estimation process itself. Because the point estimation is already complex due to variable selection or penalization, the variance estimation must be "aware" of these complexities, rather than treating the point estimate as a simple, fixed quantity derived from a low-dimensional model. While bias correction is a primary focus of new methods, the stability and computational cost of these advanced variance estimators are also critical practical considerations, particularly for NSOs that require reliable and timely production of estimates.
The following table provides a comparative overview of variance estimation techniques in high-dimensional survey settings:
Table 3: Comparative Overview of Variance Estimation Techniques in High-Dimensional Settings

Variance Estimation Technique	Brief Description of Mechanism	Performance in High Dimensions (Bias, Efficiency)	Suitability for Complex Survey Designs	Key Challenges/Assumptions	Illustrative References	
Standard Taylor Linearization	Uses a first-order Taylor series expansion to approximate the variance of a non-linear estimator.	Often substantially underestimates variance when p is large relative to n.	Widely used, but requires careful derivation for each estimator and design.	Assumes smoothness, relies on good behavior of residuals which fails in high-D.	1	
Standard Jackknife	A resampling method that repeatedly omits one (or a group of) observation(s) to estimate variance.	Often substantially overestimates variance when p is large relative to n.	Generally applicable to complex designs, but can be computationally intensive.	Assumes estimator stability; overestimation due to inflated variance of jackknife residuals in high-D.	1	
Bias-Adjusted Taylor/Jackknife	Modifies standard Taylor or Jackknife estimators to correct for the identified high-dimensional bias.	Significantly reduces bias, performs well even for large p/n ratios.	Adaptable to model-assisted (GREG) and imputation estimators under certain designs (e.g., SRS, Bernoulli).	Adjustments can depend on unknown quantities requiring estimation; theory less developed for all complex designs.	1	
Refitted Cross-Validation (RCV)	Two-stage refitted procedure using data splitting to attenuate influence of irrelevant variables with spurious correlations.	Aims for oracle-like performance; reduces underestimation of noise level caused by spurious variable selection.	Primarily developed for linear regression settings; adaptation to survey context is an area of research.	Requires data splitting, choice of initial variable selection method.	19	
Natural Adaptive Elastic-Net (NAEN)	Solves a re-parameterized log-likelihood with adaptive elastic-net to simultaneously estimate regression and variance parameters.	Performs well in moderately sparse high-D scenarios with many non-zero coefficients; close to oracle.	Developed for linear models; integration with complex survey designs needs further exploration.	Relies on tuning parameters; performance may be suboptimal in extremely sparse settings compared to other specialized methods.	30	
4.1 Proposed Bias-Adjusted Variance Estimators
Recognizing the substantial bias of traditional variance estimators in high-dimensional contexts, researchers have focused on developing bias-adjusted versions. These estimators aim to correct the systematic errors observed in Taylor linearization and jackknife methods when applied to estimators (like GREG or imputation-based estimators) that use high-dimensional auxiliary data.1 The adjustments typically involve modifying the terms in the variance formula to account for the impact of high dimensionality on quantities like residuals or g-weights. For instance, bias-adjusted Taylor, g-weighted, and jackknife variance estimators have been proposed for the GREG estimator and for estimators based on deterministic linear regression imputation. Empirical studies and theoretical analyses (under certain sampling designs like Bernoulli sampling or simple random sampling without replacement) have shown that these bias-adjusted estimators can perform very well, often exhibiting low relative bias even when the ratio p/n is large.1
4.2 Refitted Cross-Validation (RCV) Techniques
Another avenue for improving variance estimation in high-dimensional regression settings, which are often implicit in model-assisted survey estimation, is the use of Refitted Cross-Validation (RCV).19 This approach involves a two-stage refitted procedure that utilizes data splitting. The primary goal of RCV is to mitigate the influence of irrelevant predictor variables that happen to be spuriously correlated with the noise term in the model. Such spurious correlations can lead to these irrelevant variables being incorrectly selected by variable selection procedures, and their inclusion can cause a serious underestimation of the true error variance (noise level). The RCV method aims to produce a variance estimate that performs as well as an "oracle" estimator, which would theoretically know the true mean regression function in advance. It has been shown that RCV can improve upon more naive two-stage variance estimators or plug-in estimators derived from penalized regression methods like Lasso or SCAD.19
4.3 Natural Adaptive Elastic-Net (NAEN) for Variance Estimation
The Natural Adaptive Elastic-Net (NAEN) is a more recent development specifically designed for variance estimation in high-dimensional linear models, particularly when the true underlying regression parameter vector has many non-zero elements (i.e., is not extremely sparse).30 NAEN tackles the problem by solving a re-parameterized log-likelihood optimization problem that incorporates an adaptive elastic-net penalty. A key feature of NAEN is its ability to simultaneously estimate the regression coefficients and the error variance. It inherits the advantages of the naive adaptive elastic-net, such as handling multicollinearity and performing variable selection. Simulation studies have indicated that NAEN can outperform other methods like Scaled Lasso (SL) and Natural Lasso (NL) in moderately sparse high-dimensional scenarios, with its performance closely tracking that of an oracle estimator.30 The NAEN estimator for the regression coefficients is equivalent to the solution of a naive adaptive elastic-net problem, and the NAEN variance estimator is related to the optimal value of that same problem, which simplifies its implementation.30
5. The Role of Machine Learning in Modern Survey Estimation
Machine learning (ML) methods are increasingly being explored and adapted for various stages within the survey sampling process, offering powerful tools to handle the complexity and high dimensionality of modern datasets.6 This adoption represents a significant methodological shift, moving beyond traditional, often linear, models towards more flexible, data-driven approaches. However, this transition is not without its challenges, as it requires careful adaptation of ML techniques to preserve the inferential integrity that is paramount in survey statistics. A key tension exists between the primary goal of many ML algorithms—optimizing predictive accuracy on observed data—and the core objectives of survey sampling, which include producing unbiased or consistent estimates of finite population parameters and constructing valid confidence intervals.21 Simply maximizing predictive performance on a sample, especially a complex survey sample, might not yield valid inferences for the target population if the survey design is not appropriately considered. Furthermore, the "black box" nature of some sophisticated ML models can be a barrier to their adoption in fields like official statistics, where transparency and interpretability of methods and results are highly valued.5 Consequently, research into interpretable ML and methods for robust uncertainty quantification (variance estimation) for ML-based survey estimates is critical.
5.1 Tree-based Methods (Regression Trees, Random Forests), Boosting
Tree-based methods, including single regression trees, Random Forests (an ensemble of trees), and boosting algorithms (which sequentially combine weak learners like trees), have found applications in survey estimation for tasks such as imputing missing data, estimating propensity scores for nonresponse adjustment, and serving as the predictive model in model-assisted estimation frameworks.17
●	Advantages: These methods are adept at capturing complex non-linear relationships and interactions between variables without requiring explicit pre-specification by the analyst. Random Forests, by averaging predictions from many diverse trees, can improve prediction accuracy and reduce the risk of overfitting compared to a single decision tree.25 Boosting algorithms iteratively refine predictions by focusing on observations that are difficult to predict, often leading to highly accurate models.
●	Design-Consistent Random Forests: A significant development is the creation of Random Forest algorithms specifically adapted for complex survey data.39 Standard Random Forests typically assume i.i.d. data. When applied to survey data collected via informative sampling designs, they can produce biased estimates. Design-consistent Random Forests address this by incorporating survey weights directly into the tree construction and prediction process, for example, by using weighted averages for end-node estimates (e.g., using Hájek-type estimators at the leaves of the trees). This makes the resulting forest estimator asymptotically design-unbiased and consistent, allowing for more valid predictions for populations sampled with complex designs.39
5.2 Deep Learning (DL) Approaches
Deep Learning, a subfield of ML characterized by neural networks with multiple layers (deep architectures), is being explored for its potential to model highly complex, hierarchical, and non-linear data structures in the survey context.25
●	Applications: DL models are being investigated for imputation of missing data (particularly in high-dimensional settings with non-linear relationships), propensity score estimation, and, more recently, for causal inference from observational survey data. Some studies suggest that DL-based approaches, such as those using XGBoosting (a gradient boosting algorithm often employing tree-based learners) or other deep neural network architectures, can outperform traditional methods in handling high-dimensional non-linear model structures, particularly in balancing bias and variance for tasks like missing data imputation.25
●	Causal-StoNet: An example of a specialized DL architecture is the Causal-StoNet, which employs stochastic neural networks and sparse learning principles for causal inference with high-dimensional, complex data.43 This approach is designed to handle unknown functional forms between variables and can also accommodate missing data under both Missing At Random (MAR) and Missing Not At Random (MNAR) mechanisms.
5.3 Incorporating Complex Survey Design Features into ML Models
A fundamental challenge in applying ML to survey data is that most ML algorithms are developed under the assumption of simple random sampling (i.e., i.i.d. data) and do not inherently account for essential survey design features such as unequal sampling probabilities (reflected in survey weights), stratification, or cluster sampling.21 Ignoring these features can lead to biased model parameters and predictions that do not accurately generalize to the target population from which the survey sample was drawn.
Several approaches are being investigated to address this:
●	Modifying Algorithms to Incorporate Weights: Some ML algorithms can be adapted to incorporate survey weights. For example, tree-based methods might use weighted splitting criteria to determine how to partition the data at each node, or weighted averages can be used when calculating predictions at the terminal nodes.39 Loss functions in neural networks or gradient boosting machines can also be weighted to give more influence to observations with higher survey weights.21
●	Using Survey Design Variables as Predictors: An alternative or complementary strategy is to include variables that define the survey design (e.g., stratum identifiers, cluster identifiers, or even the survey weights themselves or correlates thereof) as predictor variables within the ML model.20 The rationale is that if these design variables are related to the outcome, including them in the model can help account for the design effects.
●	Post-hoc Adjustments or Evaluations: If direct incorporation of design features into the ML algorithm is not feasible (e.g., due to software limitations), post-hoc adjustments or evaluations can be considered. For instance, an ML model might be trained without weights, but its predictive performance can then be evaluated on the survey data using weighted metrics to get a more accurate assessment of its generalizability to the target population.21
Properly accounting for complex survey design features is crucial not only for ensuring that ML model predictions are valid for the intended population but also for enabling legitimate design-based or model-assisted inference using the outputs of these models.21
6. Robustness and Causal Inference in High-Dimensional Survey Data
Beyond predictive accuracy and efficient estimation of population parameters, two increasingly important considerations in the analysis of high-dimensional survey data are the robustness of estimates to data anomalies and the potential for drawing causal inferences.
6.1 Robust Estimation Techniques
High-dimensional data, by its very nature, can be more susceptible to the influence of outliers, heavy-tailed error distributions, or other forms of data contamination or heterogeneity that can unduly affect classical estimators.9 Even penalized least squares methods, while handling high dimensionality, can lose efficiency or yield biased results in the presence of such irregularities.9 Robustness in this context is not merely about handling isolated outliers but also about addressing data heterogeneity and potential model misspecification, which become more pronounced and harder to detect when dealing with a multitude of variables. Robust methods are therefore essential for ensuring that survey estimates accurately reflect the characteristics of the bulk of the population and are not disproportionately driven by a few influential data points or by misspecified aspects of a complex high-dimensional model.
Several approaches to robust estimation in high-dimensional settings have been proposed:
●	Weight Shrinkage Methods (e.g., PAWLS): The Penalized Adaptive Weighted Least Squares (PAWLS) method offers a framework for robust regression in high dimensions.9 It associates an individual weight with each observation, where weights less than 1 indicate potential irregularity (e.g., outlier status or heterogeneity). By applying L1-type regularization (Lasso penalty) to both the regression coefficients and these observation weights, PAWLS can simultaneously perform variable selection (identifying important predictors) and outlier/irregularity detection (down-weighting or identifying influential observations). This approach has been linked to robust M-estimation and has demonstrated strong theoretical properties, including non-asymptotic oracle inequalities for the joint estimation of coefficients and weights.9
●	M-estimation: M-estimators form a general class of robust estimators that limit the influence of any single observation by modifying the objective function being minimized.9 Instead of minimizing the sum of squared residuals (as in ordinary least squares), M-estimators minimize a sum of a less rapidly increasing function of the residuals. The Huber loss function is a well-known example, which behaves like a quadratic loss for small residuals and a linear loss for large residuals, thereby down-weighting the impact of observations with large deviations.46
●	Robust Mean Estimation: Specific methods have been developed for robustly estimating the mean vector in high dimensions when a fraction of the data points may be arbitrarily corrupted. Some approaches formulate this as an optimization problem, such as minimizing the L0-norm (count) of an outlier indicator vector, subject to constraints on the data. This L0-norm can be relaxed to an Lp-norm (0<p≤1) for computational tractability.45
●	Robust Factor Models: In situations where high-dimensional data exhibit strong dependencies (e.g., financial data, genomic data), factor models are often employed. High-dimensional robust factor analysis, for instance using robust versions of PCA, can help to identify underlying latent factors while being resilient to heavy-tailed distributions or heterogeneity in the data.34
●	General Robust Machine Learning: More broadly, the field of robust machine learning aims to develop algorithms whose performance remains stable and reliable even when the input data is subject to noise, perturbations, or distributional shifts.47
6.2 Challenges and Methods for Causal Inference with High-Dimensional Survey Data
A major ambition for survey research, particularly with the advent of rich, high-dimensional auxiliary data, is to move beyond descriptive statistics and associative analyses towards estimating causal effects of specific interventions, exposures, or policies on outcomes of interest using observational survey data.49 However, drawing causal inferences from such data is fraught with challenges, especially in high-dimensional settings. The core difficulty lies in adequately controlling for confounding – the phenomenon where a third variable is associated with both the exposure and the outcome, creating a spurious association between them.
Key challenges include:
●	Confounder Selection: With a vast number of potential covariates available, identifying the true set of confounders that must be controlled for is a formidable task. Standard variable selection techniques focused on prediction may not be optimal for causal inference, as confounder selection requires identifying variables related to both the exposure (or treatment assignment) and the outcome.49
●	Defining Interpretable Estimands: When dealing with high-dimensional exposures (e.g., environmental mixtures, genetic profiles) or complex treatments, defining a causal effect (estimand) that is both scientifically meaningful and interpretable can be difficult. Dimension reduction of the exposure itself may be necessary, but this must be done carefully to preserve causal interpretation.49
●	Validity of Causal Assumptions: Causal inference relies on strong, often untestable, assumptions such as ignorability (all common causes of exposure and outcome are measured and controlled for) and overlap (or positivity, ensuring individuals have a non-zero probability of receiving each exposure level within strata of confounders). Justifying and assessing the plausibility of these assumptions becomes significantly harder when dealing with a large and complex set of variables.43
●	Spurious Correlations, Endogeneity, and Noise Accumulation: High-dimensional data are prone to spurious correlations, potential endogeneity (where predictors are correlated with the error term), and noise accumulation, all of which can obscure true causal relationships and bias effect estimates.50
Despite these challenges, several methodological approaches are being developed and applied:
●	Dimension Reduction and Variable Selection for Confounders: Techniques such as PCA or specialized variable selection algorithms designed for causal inference are used to select a manageable and relevant set of confounders from a high-dimensional pool.49
●	High-Dimensional Propensity Score Methods: Propensity scores (the probability of receiving treatment conditional on observed covariates) are widely used to adjust for confounding. Machine learning methods are increasingly employed to estimate propensity scores when the number of covariates is large.43
●	Double Machine Learning (DML): DML is a framework that uses ML algorithms to estimate "nuisance functions" (e.g., the conditional mean of the outcome given covariates, and the conditional probability of treatment given covariates) in a way that is robust to biases from regularization.50 It often employs techniques like cross-fitting and orthogonalization to construct causal effect estimators that are less sensitive to imperfections in the estimation of these nuisance functions.
●	Deep Learning for Causal Inference (e.g., Causal-StoNet): As mentioned earlier, DL architectures like Causal-StoNet are being developed to model complex relationships in observational data, estimate average treatment effects (ATE), and simultaneously handle high-dimensional covariates, unknown functional forms, and missing data.43
●	Covariate Balance: Achieving balance in the distribution of observed covariates between treated and untreated groups (after adjustment) is a key diagnostic for successful confounding control. Methods like Approximate Residual Balancing (ARB), Bayesian Additive Regression Trees (BART), and DML incorporate mechanisms or checks to promote covariate balance in high-dimensional settings.50
The interplay between methods for robust estimation, missing data handling, and causal inference is strong. For instance, robust estimation of propensity scores is vital if causal inference is to be performed in the presence of outliers or influential observations in the covariate data. Similarly, missing data in potential confounders must be appropriately handled, often using high-dimensional imputation techniques, before causal effects can be reliably estimated. These techniques are rarely used in isolation but form components of a larger, often complex, analytical pipeline for drawing causal conclusions from high-dimensional survey data.
7. Future Research Horizons and Priorities
The field of high-dimensional estimation in survey sampling is dynamic and rapidly evolving. While significant progress has been made, numerous challenges and open questions remain, defining a rich agenda for future research. The trajectory of this research is increasingly intertwined with broader trends in data science, particularly the rise of machine learning, artificial intelligence, and the growing availability of diverse, non-traditional data sources.6 Survey methodology must continue to evolve by integrating these advancements rather than operating in isolation. A persistent theme across future research priorities is the tension between methodological sophistication and practical adoptability, especially for NSOs and other organizations that rely on survey data for official statistics or critical decision-making.6 Therefore, future work needs to emphasize not only theoretical novelty but also computational efficiency, ease of implementation, and robust performance in real-world survey conditions. Furthermore, as models become more complex and data sources more varied, addressing concerns related to the "replication crisis" and ensuring the trustworthiness of findings will become even more critical. This implies a greater emphasis on rigorous validation techniques, comprehensive uncertainty quantification, and the clear articulation of underlying assumptions.52
The following table outlines key future research priorities:
Table 4: Future Research Priorities in High-Dimensional Survey Estimation

Research Area	Key Unresolved Questions/Objectives	Potential Impact on Survey Practice	Illustrative References	
Robust & Efficient Estimators	Developing estimators more resilient to model misspecification, outliers, and complex dependencies under survey designs; improving bias/efficiency in ultra-high-D.	More reliable estimates in the face of imperfect data and models; better performance when p≫n.	9	
Complex Survey Design Integration	Seamless and theoretically sound integration of weights, stratification, clustering into advanced statistical/ML models; robust variance estimation for these.	More accurate and valid inferences from complex surveys using modern methods; reliable uncertainty measures.	20	
Causal Inference	Refining confounder selection from many variables; high-D mediation analysis; assessing causal assumptions in complex survey settings.	Enabling more policy-relevant conclusions from observational survey data; better understanding of causal mechanisms.	49	
Non-Probability Sample Integration	Methods for high-D estimation with non-probability samples (bias adjustment, variance); integrating probability and non-probability data sources.	Leveraging diverse data sources while managing bias; potentially reducing costs and improving timeliness.	6	
Computational Scalability & Practicality	Developing algorithms feasible for NSO-scale datasets; user-friendly software; automated/robust tuning parameter selection.	Enabling routine use of advanced methods by practitioners; improving timeliness and cost-effectiveness of survey production.	6	
Interpretable Estimands	Ensuring quantities estimated by complex ML models or from high-D exposures are meaningful and interpretable for policy/science.	Enhancing the utility and actionability of survey findings derived from sophisticated models.	49	
Interval Estimation for Penalized Models	Developing valid confidence intervals for parameters from penalized regression, addressing post-selection inference and bias.	Providing reliable measures of uncertainty for sparse models common in high-D settings.	26	
Key areas for future investigation include:
●	Continued Development of Robust and Efficient Estimators: There is an ongoing need for estimators that are not only efficient in leveraging high-dimensional auxiliary information but are also robust to deviations from idealized assumptions, such as model misspecification, the presence of outliers, or complex dependency structures within the data, particularly when these are encountered under complex survey designs.9 Improving the bias and variance properties of estimators in ultra-high dimensional settings (where p≫n) remains a significant challenge.
●	Advanced Methods for Incorporating Complex Survey Designs: While progress has been made, particularly with methods like design-consistent random forests 39, further research is needed to develop more general and theoretically sound frameworks for integrating survey weights, stratification, and clustering effects into a wider array of advanced statistical and machine learning models.20 A critical component of this is the development of reliable variance estimation procedures for these complex estimators when applied to data from complex surveys.52
●	Causal Inference with Observational Survey Data in High Dimensions: The pursuit of causal claims from observational survey data is a high-priority area. Future research should focus on refining methods for selecting and controlling for confounders from a vast pool of potential variables, developing robust approaches for high-dimensional mediation analysis to understand causal pathways, and establishing clearer guidelines and diagnostic tools for assessing the plausibility of core causal identifying assumptions (e.g., ignorability, overlap) in the context of complex, high-dimensional survey data.43
●	Leveraging Non-Probability Samples and Integrating Diverse Data Sources: The survey landscape is increasingly characterized by the availability of non-probability samples (e.g., web panels, opt-in data) and large-scale administrative or commercial datasets, often with high-dimensional features.6 Developing statistically sound methods for high-dimensional estimation using such non-probability samples, including robust techniques for bias adjustment and variance estimation, is crucial. Furthermore, research into data integration techniques that can effectively combine information from smaller, high-quality probability surveys with larger, potentially biased, but high-dimensional non-probability or administrative datasets will be vital for enhancing the richness and timeliness of statistical information.
●	Improving Computational Scalability and Practical Implementation for NSOs: For advanced high-dimensional methods to be adopted by NSOs and other survey practitioners, they must be computationally feasible for the very large datasets and extensive auxiliary information that these organizations increasingly encounter.6 This includes the development of scalable algorithms, user-friendly and well-documented software implementations, and practical guidance on complex issues like the robust and, where possible, automated selection of tuning parameters for penalized or ML-based methods.
●	Defining and Estimating Interpretable Estimands: As statistical models become more complex, particularly with the use of ML algorithms or when dealing with high-dimensional exposures (e.g., the combined effect of many environmental pollutants), it is essential to ensure that the quantities being estimated (the estimands) are clearly defined, scientifically meaningful, and interpretable for end-users, such as policymakers or the public.49
●	Interval Estimation in Penalized Models: While penalized regression methods are powerful tools for estimation and variable selection in high dimensions, constructing valid confidence intervals for the selected parameters remains a challenge due to the effects of shrinkage and the selection process itself (post-selection inference).26 Continued research into debiasing techniques and robust methods for interval estimation in these contexts is needed.
8. Concluding Remarks and Strategic Recommendations
The integration of high-dimensional auxiliary information into survey sampling represents a paradigm shift, offering unprecedented opportunities for enhancing the precision and scope of statistical estimates while simultaneously presenting profound methodological and computational challenges. Significant advancements have been made in developing and adapting techniques such as penalized regression, machine learning algorithms, and bias-adjusted variance estimators to navigate this complex landscape. These tools provide pathways to manage issues like overfitting, multicollinearity, and the instability of traditional estimators when faced with a large number of auxiliary variables. The field is in a dynamic phase of rapid evolution, driven by both the allure of new data sources and the inherent complexities of high dimensionality. This necessitates a new synthesis that thoughtfully combines classical survey principles with modern statistical learning and computational techniques.
Despite this progress, persistent challenges remain. The robust incorporation of complex survey design features (weights, stratification, clustering) into these advanced models is an ongoing area of research. Drawing valid causal inferences from high-dimensional observational survey data continues to be a difficult endeavor, requiring careful attention to assumptions and methodological rigor. Furthermore, the practical implementation of these sophisticated methods, particularly within the operational constraints of NSOs, requires further development in terms of computational scalability, user-friendly software, and clear guidance for practitioners.
Ultimately, the fundamental goal of survey sampling—to produce reliable, accurate, and relevant information about populations—remains unchanged.51 High-dimensional estimation methods are powerful tools that can help achieve this goal more effectively in the current data-rich environment. However, their application must be guided by the foundational principles of good statistical practice, including clear definitions of estimands, rigorous assessment of assumptions, careful attention to bias and variance, and the transparent communication of uncertainty.
Recommendations for Practitioners:
●	Embrace Continuous Learning: The field is evolving rapidly; practitioners should actively engage with new methodological developments and their implications.
●	Prioritize Understanding Assumptions: Before applying any new high-dimensional technique, it is crucial to understand its underlying assumptions, limitations, and the contexts in which it is expected to perform well.
●	Advocate for and Adopt Appropriate Software: Utilize and encourage the development of software tools that correctly implement advanced methods while properly accounting for complex survey design features.
●	Focus on Robust Validation and Uncertainty Communication: Rigorously validate models and estimates, for example, through cross-validation or sensitivity analyses, and clearly communicate the associated uncertainties to end-users.
Recommendations for Researchers:
●	Address Identified Future Research Priorities: Focus efforts on the key unresolved questions outlined, particularly in areas like robust integration of survey designs, causal inference, and handling non-probability samples.
●	Foster Collaboration: Engage in collaborations with NSOs and other survey practitioners to ensure that new methods are not only theoretically sound but also practically relevant, computationally feasible, and address real-world operational needs.
●	Develop Unified Theoretical Frameworks: Strive to develop more encompassing theoretical frameworks that can unify the treatment of diverse data types (probability samples, non-probability samples, administrative data), complex survey designs, and a range of estimation goals within the high-dimensional context.
By addressing these challenges and pursuing these research directions, the field of survey sampling can continue to adapt and thrive, leveraging the power of high-dimensional data to provide deeper and more accurate insights into society.
Works cited
1.	On high‐dimensional variance estimation in survey sampling - ResearchGate, accessed June 5, 2025, https://www.researchgate.net/publication/390165336_On_high-dimensional_variance_estimation_in_survey_sampling
2.	Tackling High-Dimensional Data Challenges - Number Analytics, accessed June 5, 2025, https://www.numberanalytics.com/blog/high-dimensional-data-challenges
3.	Statistics for High-Dimensional Data.pdf, accessed June 5, 2025, https://www.stat.ntu.edu.tw/download/%E6%95%99%E5%AD%B8%E6%96%87%E4%BB%B6/bigdata/Statistics%20for%20High-Dimensional%20Data.pdf
4.	High-dimensional estimation in a survey sampling framework, model-assisted and calibration points of view - IDEAS/RePEc, accessed June 5, 2025, https://ideas.repec.org/a/spr/metron/v83y2025i1d10.1007_s40300-024-00280-9.html
5.	Survey Methodology 50-2, accessed June 5, 2025, https://publications.gc.ca/collections/collection_2024/statcan/12-001-x/12-001-x2024002-eng.pdf
6.	No. 90 July 2024 - International Association of Survey Statisticians (IASS), accessed June 5, 2025, https://isi-iass.org/home/wp-content/uploads/Survey_Statistician_2024_July_N90.pdf
7.	arxiv.org, accessed June 5, 2025, https://arxiv.org/pdf/2401.07625
8.	Navigating Complexity: Techniques to Simplify High-Dimensional Data Analysis, accessed June 5, 2025, https://www.numberanalytics.com/blog/navigating-high-dimensional-data-complexity
9.	core.ac.uk, accessed June 5, 2025, https://core.ac.uk/download/pdf/345082776.pdf
10.	A Selective Overview of Variable Selection in High Dimensional ..., accessed June 5, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC3092303/
11.	Multicollinearity in Regression Analysis: Problems, Detection, and Solutions, accessed June 5, 2025, https://statisticsbyjim.com/regression/multicollinearity-in-regression-analysis/
12.	Estimation of Finite Population Totals in High Dimensional Spaces, accessed June 5, 2025, https://www.scirp.org/journal/paperinformation?paperid=120334
13.	On high‐dimensional variance estimation in survey sampling, accessed June 5, 2025, https://ideas.repec.org/a/bla/scjsta/v52y2025i2p924-959.html
14.	On the Computational Complexity of Private High-dimensional Model Selection | OpenReview, accessed June 5, 2025, https://openreview.net/forum?id=PzG7xVlYqm&referrer=%5Bthe%20profile%20of%20Saptarshi%20Roy%5D(%2Fprofile%3Fid%3D~Saptarshi_Roy1)
15.	A Survey of Methods in Variable Selection and Penalized Regression - SAS Support, accessed June 5, 2025, https://support.sas.com/resources/papers/proceedings20/4287-2020.pdf
16.	Penalized Least Squares Regression: Fast Computation via Efficient Approximation - Purdue Department of Statistics, accessed June 5, 2025, https://www.stat.purdue.edu/~chong/ps/kim2.pdf
17.	Model-assisted estimation in high-dimensional settings for survey ..., accessed June 5, 2025, https://www.researchgate.net/publication/359305642_Model-assisted_estimation_in_high-dimensional_settings_for_survey_data
18.	Asymptotic efficiency of the calibration estimator in a high ..., accessed June 5, 2025, https://www.researchgate.net/publication/353554130_Asymptotic_efficiency_of_the_calibration_estimator_in_a_high-dimensional_data_setting
19.	Variance Estimation Using Refitted Cross-Validation in Ultrahigh ..., accessed June 5, 2025, https://academic.oup.com/jrsssb/article/74/1/37/7074999
20.	Struggles with Survey Weighting and Regression Modeling - Columbia University, accessed June 5, 2025, https://sites.stat.columbia.edu/gelman/research/published/STS226.pdf
21.	Implementing machine learning methods with complex survey data ..., accessed June 5, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC9838837/
22.	Statistical inference with weights and survey design variables, accessed June 5, 2025, https://ukdataserviceopen.github.io/DSP-core-inference/UKDS_weighting_current.html
23.	Package 'survey' reference manual - R-Forge, accessed June 5, 2025, https://r-forge.r-universe.dev/survey/doc/manual.html
24.	Handling Missing Values in Surveys With Complex Study Design: A ..., accessed June 5, 2025, https://academic.oup.com/jssam/article/12/1/105/7048720
25.	Handling high-dimensional data with missing values by modern ..., accessed June 5, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC9930810/
26.	Interval Estimation of Coefficients in Penalized Regression Models of Insurance Data - arXiv, accessed June 5, 2025, https://arxiv.org/html/2410.01008v3
27.	JSM 2018 Online Program - American Statistical Association, accessed June 5, 2025, https://ww2.amstat.org/meetings/jsm/2018/onlineprogram/AbstractDetails.cfm?abstractid=330097
28.	Model selection procedure for high-dimensional data - PMC, accessed June 5, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC2992390/
29.	A Survey on Rough Feature Selection: Recent Advances and Challenges, accessed June 5, 2025, https://www.ieee-jas.net/en/article/doi/10.1109/JAS.2025.125231
30.	home.cc.umanitoba.ca, accessed June 5, 2025, http://home.cc.umanitoba.ca/~wangl1/papers/2023jimo.pdf
31.	On the adaptive elastic-net with a diverging number of parameters - Project Euclid, accessed June 5, 2025, https://projecteuclid.org/journals/annals-of-statistics/volume-37/issue-4/On-the-adaptive-elastic-net-with-a-diverging-number-of/10.1214/08-AOS625.pdf
32.	arxiv.org, accessed June 5, 2025, https://arxiv.org/pdf/2405.14652
33.	Weighted Lasso Estimates for Sparse Logistic Regression: Non-asymptotic Properties with Measurement Error - arXiv, accessed June 5, 2025, https://arxiv.org/pdf/2006.06136
34.	Robust high dimensional factor models with applications to statistical machine learning - PMC - PubMed Central, accessed June 5, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC8315369/
35.	Sure Independence Screening | Request PDF - ResearchGate, accessed June 5, 2025, https://www.researchgate.net/publication/352325301_Sure_Independence_Screening
36.	Inference on High Dimensional Selective Labeling Models - cireq, accessed June 5, 2025, https://cireqmontreal.com/wp-content/uploads/2024/09/khan.pdf
37.	Variance Estimation Using Refitted Cross-validation in Ultrahigh Dimensional Regression | Request PDF - ResearchGate, accessed June 5, 2025, https://www.researchgate.net/publication/386972935_Variance_Estimation_Using_Refitted_Cross-validation_in_Ultrahigh_Dimensional_Regression
38.	Random forest - Wikipedia, accessed June 5, 2025, https://en.wikipedia.org/wiki/Random_forest
39.	www150.statcan.gc.ca, accessed June 5, 2025, https://www150.statcan.gc.ca/n1/pub/12-001-x/2024002/article/00015-eng.pdf
40.	Machine Learning Assisted Complex Survey Weights, accessed June 5, 2025, https://www.fcsm.gov/assets/files/docs/I5Kolenikov.pdf
41.	Calibration and XGBoost reweighting to reduce coverage and non-response biases in overlapping panel surveys - PubMed Central, accessed June 5, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC10868104/
42.	Instance-Based Uncertainty Estimation for Gradient-Boosted Regression Trees - University of Oregon, accessed June 5, 2025, https://ix.cs.uoregon.edu/~lowd/brophy-neurips22.pdf
43.	Causal-StoNet: Causal Inference for High-Dimensional Complex Data - arXiv, accessed June 5, 2025, https://arxiv.org/html/2403.18994v1
44.	arxiv.org, accessed June 5, 2025, https://arxiv.org/pdf/2403.18994
45.	Robust Mean Estimation in High Dimensions: An Outlier-Fraction Agnostic and Efficient Algorithm - arXiv, accessed June 5, 2025, https://arxiv.org/pdf/2102.08573
46.	7 Key Statistical Insights into Robust Regression Methods - Number Analytics, accessed June 5, 2025, https://www.numberanalytics.com/blog/7-statistical-insights-robust-regression-methods
47.	monk1337/Awesome-Robust-Machine-Learning - GitHub, accessed June 5, 2025, https://github.com/monk1337/Awesome-Robust-Machine-Learning
48.	Chapter 0 Machine Learning Robustness: A Primer - arXiv, accessed June 5, 2025, https://arxiv.org/html/2404.00897v2
49.	The Future of Causal Inference - PMC, accessed June 5, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC9991894/
50.	oulurepo.oulu.fi, accessed June 5, 2025, https://oulurepo.oulu.fi/bitstream/handle/10024/53646/nbnfioulu-202501131133.pdf?sequence=1&isAllowed=y
51.	Future of Survey Sampling | Public Opinion Quarterly | Oxford ..., accessed June 5, 2025, https://academic.oup.com/poq/article/75/5/872/1823136
52.	No. 91 January 2025 - International Association of Survey Statisticians (IASS), accessed June 5, 2025, https://isi-iass.org/home/wp-content/uploads/Survey_Statistician_2025_January_N91.pdf
53.	Bayesian estimation methods for survey data with potential applications to health disparities research Article - arXiv, accessed June 5, 2025, https://arxiv.org/pdf/2303.04996
54.	The Future of Survey Sampling - Portal de Periódicos da CAPES, accessed June 5, 2025, https://www.periodicos.capes.gov.br/index.php/acervo/buscador.html?task=detalhes&id=W2161470413
55.	THE FUTURE OF SURVEY SAMPLING - Middlebury College, accessed June 5, 2025, https://miislibrarysearch.middlebury.edu/discovery/fulldisplay?docid=cdi_proquest_miscellaneous_1038901359&context=PC&vid=01MIDDLE_INST:01MIDDLE_INST_cm&lang=en&search_scope=MIISCAMPUS&adaptor=Primo%20Central&tab=Campus&query=creator%2Cequals%2CBrick%2C%20J.%20Michael%20%2CAND&mode=advanced&offset=0