Consistent covariate selection and post model selection inference in semiparametric regression

2004/05/27 by Florentina Bunea · 4 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Statistical Methods and Inference #math.ST #msc:62F99 #msc:62G05 #msc:62G08 #msc:62J02 #stat.TH

paper · pdf · doi:10.1214/009053604000000247

published as Annals of Statistics 2004, Vol. 32, No. 3, 898-927

openalex publication_date 2004/05/27 · arxiv created 2004/06/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=β^′\underlineX_i+f(T_i)+W_i , i=1,…,n. The parametric and nonparametric components are estimated simultaneously by this procedure. Estimation is based on a collection of finite-dimensional models, using a penalized least squares criterion for selection. We show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models, we can consistently estimate the subset of nonzero coefficients of the linear part. Moreover, the selected estimator of the linear component is asymptotically normal.

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