设计辅助回归

中文摘要 AI 辅助

我们考虑回归问题，其中协变量的边际分布对估计和变量选择具有信息性，而不仅仅是辅助性的。受随机设计、高维和潜在效应设置的启发，我们提出了一个通用的设计辅助回归框架，其中估计准则依赖于 $Y \mid \bfX$ 的条件模型和协变量分布的结构化特征。该框架识别了设计信息的两个作用：通过二次正则化稳定弱设计方向，以及通过干扰增强校正潜在效应失真。我们建立了所得估计量的oracle性质，分离了随机误差、收缩和近似的影响，并将其与忽略设计信息的基准稀疏程序进行比较。这些结果表明，所提出的框架在保持一阶预测性能的同时提高了估计效果。数值研究和两个真实数据应用说明了纳入设计信息的实际影响。

英文摘要

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 $Y \mid \bfX$ 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.

发表机构

• Florida International University（佛罗里达国际大学）
• The Dartmouth Institute for Health Policy and Clinical Practice, Geisel School of Medicine, Dartmouth College（达特茅斯学院盖泽尔医学院达特茅斯健康政策与临床实践研究所）
• School of Economics, University of Nottingham Ningbo China（宁波诺丁汉大学经济学院）
• Oklahoma State University（俄克拉荷马州立大学）

机构由 AI 辅助整理，请以论文原文为准。