Subsampling for Big Data Linear Models with Measurement Errors

TL;DR

This paper develops and analyzes two subsampling algorithms for large-scale linear regression models with measurement errors, providing theoretical insights and demonstrating their effectiveness through simulations and real data examples.

Contribution

It introduces two novel subsampling algorithms that account for measurement errors in large datasets, extending existing methods to more realistic scenarios.

Findings

Both algorithms are theoretically justified.

Numerical simulations show improved accuracy.

Real data examples confirm practical effectiveness.

Abstract

Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical applications, the observed covariates may suffer from inaccuracies due to measurement errors. To address the challenge of large datasets with measurement errors, this study explores two subsampling algorithms based on the corrected likelihood approach: the optimal subsampling algorithm utilizing inverse probability weighting and the perturbation subsampling algorithm employing random weighting assuming a perfectly known distribution. Theoretical properties for both algorithms are provided. Numerical simulations and two real-world examples demonstrate the effectiveness of these proposed methods compared to other uncorrected algorithms.