Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Penalized least squares for single index models

Language

English

Abstract

The single index model is a useful regression model. In this paper, we propose a nonconcave penalized least squares method to estimate both the parameters and the link function of the single index model. Compared to other variable selection and estimation methods, the proposed method can estimate parameters and select variables simultaneously. When the dimension of parameters in the single index model is a fixed constant, under some regularity conditions, we demonstrate that the proposed estimators for parameters have the so-called oracle property, and furthermore we establish the asymptotic normality and develop a sandwich formula to estimate the standard deviations of the proposed estimators. Simulation studies and a real data analysis are presented to illustrate the proposed methods. © 2010 Elsevier B.V.

Keywords

Local polynomial regression, Nonconcave penalized least squares, SCAD penalty, Single index model, Variable selection

Publication Date

2011

Source Publication Title

Journal of Statistical Planning and Inference

Volume

141

Issue

4

Start Page

1362

End Page

1379

Publisher

Elsevier

DOI

10.1016/j.jspi.2010.10.003

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.jspi.2010.10.003

ISSN (print)

03783758

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