Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification
Abstract
In many modern applications, obtaining response variables is costly, time-consuming, or technically challenging, making it impractical to measure outcomes for all available units. In such settings, covariates may be available for a large pool of candidates, but responses can only be collected for a small, carefully selected subset, making the choice of which units to measure a consequential decision. Most existing subsampling methods are developed for massive datasets, emphasizing the trade-off between statistical accuracy and computational cost, and typically relying on the assumption of a correctly specified model. These features limit their suitability in measurement-constrained settings, where statistical efficiency is paramount and model misspecification is often unavoidable. To address these challenges, we develop a new subset selection framework for linear regression that accommodates potential model misspecification. The proposed approach targets predictive expected loss and yields an A-optimality-type criterion that depends only on covariate information, requiring no response observations at the selection stage. We refer to this method as Expected Loss Optimal Selection (ELOS). By focusing on predictive risk rather than model-based optimality, ELOS remains well-defined and robust under misspecification. Simulation studies and real data applications demonstrate that ELOS achieves strong predictive performance and compares favorably with existing methods across a range of scenarios.
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BibTeX
@misc{kong2026subdata,
title = {{Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification}},
author = {Yundi Kong and Min Yang and Ping-Shou Zhong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19351},
eprint = {2610.19351},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19351},
}
RIS
TY - UNPB
TI - Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification
AU - Yundi Kong
AU - Min Yang
AU - Ping-Shou Zhong
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19351
UR - https://arxiv.org/abs/2610.19351
AB - In many modern applications, obtaining response variables is costly, time-consuming, or technically challenging, making it impractical to measure outcomes for all available units. In such settings, covariates may be available for a large pool of candidates, but responses can only be collected for a small, carefully selected subset, making the choice of which units to measure a consequential decision. Most existing subsampling methods are developed for massive datasets, emphasizing the trade-off between statistical accuracy and computational cost, and typically relying on the assumption of a correctly specified model. These features limit their suitability in measurement-constrained settings, where statistical efficiency is paramount and model misspecification is often unavoidable. To address these challenges, we develop a new subset selection framework for linear regression that accommodates potential model misspecification. The proposed approach targets predictive expected loss and yields an A-optimality-type criterion that depends only on covariate information, requiring no response observations at the selection stage. We refer to this method as Expected Loss Optimal Selection (ELOS). By focusing on predictive risk rather than model-based optimality, ELOS remains well-defined and robust under misspecification. Simulation studies and real data applications demonstrate that ELOS achieves strong predictive performance and compares favorably with existing methods across a range of scenarios.
ER -