Design-Assisted Regression
Abstract
We consider regression problems in which the marginal distribution of the covariates is informative for estimation and variable selection, rather than merely auxiliary. Motivated by random-design, high-dimensional, and latent-effect settings, we propose a general design-assisted regression framework in which the estimating criterion depends on both the conditional model for Y | bfX and structured features of the covariate distribution. The framework identifies two roles of design information: stabilizing weak design directions through quadratic regularization and correcting latent-effect distortion through nuisance augmentation. We establish oracle properties for the resulting estimator, separate the effects of stochastic error, shrinkage, and approximation, and compare it with a benchmark sparse procedure that ignores design information. These results show that the proposed framework improves estimation while preserving first-order prediction performance. Numerical studies and two real-data applications illustrate the practical impact of incorporating design information.
Related
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- Improved Variance Estimation in Homoskedastic Nonparametric Random-Design Regression via a Two-Scale Approach
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BibTeX
@misc{ye2026designassisted,
title = {{Design-Assisted Regression}},
author = {Shangyuan Ye and Guanbo Wang and Cong Zhang and Ye Liang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12886},
eprint = {2609.12886},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12886},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Design-Assisted Regression
AU - Shangyuan Ye
AU - Guanbo Wang
AU - Cong Zhang
AU - Ye Liang
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12886
UR - https://arxiv.org/abs/2609.12886
AB - We consider regression problems in which the marginal distribution of the covariates is informative for estimation and variable selection, rather than merely auxiliary. Motivated by random-design, high-dimensional, and latent-effect settings, we propose a general design-assisted regression framework in which the estimating criterion depends on both the conditional model for Y | bfX and structured features of the covariate distribution. The framework identifies two roles of design information: stabilizing weak design directions through quadratic regularization and correcting latent-effect distortion through nuisance augmentation. We establish oracle properties for the resulting estimator, separate the effects of stochastic error, shrinkage, and approximation, and compare it with a benchmark sparse procedure that ignores design information. These results show that the proposed framework improves estimation while preserving first-order prediction performance. Numerical studies and two real-data applications illustrate the practical impact of incorporating design information.
ER -