NONASYMPTOTIC ANALYSIS OF SEMIPARAMETRIC REGRESSION MODELS WITH HIGH-DIMENSIONAL PARAMETRIC COEFFICIENTS

• 成果类型: Article
• 署名作者: Zhu, Ying
• 署名单位: Michigan State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1528
• 发表日期: 2017
• 页码: 2274-2298
• 关键词: SELECTION PROCEDURES; variable selection; series estimation; sample selection; Lasso; RECOVERY; rates

摘要

We consider a two-step projection based Lasso procedure for estimating a partially linear regression model where the number of coefficients in the linear component can exceed the sample size and these coefficients belong to the l(q) -balls for q is an element of [0, 1]. Our theoretical results regarding the properties of the estimators are nonasymptotic. In particular, we establish a new nonasymptotic oracle result: Although the error of the nonparametric projection per se (with respect to the prediction norm) has the scaling t(n) in the first step, it only contributes a scaling t(n)(2) in the l(2)-error of the second-step estimator for the linear coefficients. This new oracle result holds for a large family of nonparametric least squares procedures and regularized nonparametric least squares procedures for the first-step estimation and the driver behind it lies in the projection strategy. We specialize our analysis to the estimation of a semiparametric sample selection model and provide a simple method with theoretical guarantees for choosing the regularization parameter in practice.