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Indexed by:期刊论文

Date of Publication:2010-11-01

Journal:STATISTICS & PROBABILITY LETTERS

Included Journals:SCIE、Scopus

Volume:80

Issue:21-22

Page Number:1584-1596

ISSN No.:0167-7152

Key Words:Generalized linear models; Variable selection; Bridge estimator; Oracle; Bayesian information criterion (BIC)

Abstract:Variable selection is fundamental to high dimensional generalized linear models. A number of variable selection approaches have been proposed in the literature. This paper considers the problem of variable selection and estimation in generalized linear models via a bridge penalty in the situation where the number of parameters diverges with the sample size. Under reasonable conditions the consistency of the bridge estimator can be achieved. Furthermore, it can select the nonzero coefficients with a probability converging to 1 and the estimators of nonzero coefficients have the asymptotic normality, namely the oracle property. Our simulations indicate that the bridge penalty is an effective consistent model selection technique and is comparable to the smoothly clipped absolute deviation procedure. A real example analysis is presented. (C) 2010 Elsevier B.V. All rights reserved.