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Indexed by:期刊论文

Date of Publication:2011-01-01

Journal:COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

Included Journals:Scopus、SCIE

Volume:40

Issue:24

Page Number:4325-4346

ISSN No.:0361-0926

Key Words:Bayesian information criterion; Bridge estimator; Oracle property; Partially linear model; Variable selection

Abstract:This article studies variable selection and parameter estimation in the partially linear model when the number of covariates in the linear part increases to infinity. Using the bridge penalty method, we succeed in selecting the important covariates of the linear part. Under regularity conditions, we have shown that the bridge penalized estimator of the parametric part enjoys the oracle property. We also obtain the convergence rate of the estimator of the nonparametric part. Simulation studies show that the bridge estimator performs as well as the oracle estimator for the partially linear model. An application is analyzed to illustrate the bridge procedure.