Errors-in-variables regression for dependent data with estimated error covariance matrix: To prewhiten or not?

2026-01-04

AI Summary

This study addresses the unclear efficacy of prewhitening in high-dimensional errors-in-variables regression with dependent observations and unknown error covariance structure. By leveraging weighted least squares estimation, asymptotic normality analysis, and high-dimensional covariance matrix estimation techniques, the work systematically compares the statistical efficiency and computational cost of prewhitened versus non-prewhitened estimators. The findings reveal that prewhitening does not universally improve estimation efficiency; instead, it imposes stricter sample size requirements for consistent covariance estimation and substantially increases computational burden. These results challenge the presumed broad applicability of prewhitening in high-dimensional settings with dependent data and provide theoretical guidance for method selection in practice.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We consider statistical inference for errors-in-variables regression models with dependent observations under the high dimensionality of the error covariance matrix. It is tempting to prewhiten the model and data that had led to efficient weighted least squares estimation in the presence of the measurement errors, as being practised in the optimal fingerprinting approach in climate change studies. However, it is unclear to what extent the prewhitened estimator can improve the estimation efficiency of the unprewhitened estimator for errors-in-variables regression. We compare the prewhitening and unprewhitening estimators in terms of their estimation efficiency and computational cost. It shows that while the prewhitening operation does not necessarily improve the estimation efficiency of its unprewhitening counterpart, it demands more on the ensemble size needed in the error-covariance matrix estimation to ensure the asymptotic normality, and hence it would requires much more computationally resource.

Problem

• errors-in-variables regression
• dependent data
• error covariance matrix
• prewhitening
• high dimensionality

Innovation

• errors-in-variables regression
• prewhitening
• dependent data
• high-dimensional covariance estimation
• estimation efficiency