Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Nonconcave penalized inverse regression in single-index models with high dimensional predictors

Language

English

Abstract

In this paper we aim to estimate the direction in general single-index models and to select important variables simultaneously when a diverging number of predictors are involved in regressions. Towards this end, we propose the nonconcave penalized inverse regression method. Specifically, the resulting estimation with the SCAD penalty enjoys an oracle property in semi-parametric models even when the dimension, pn, of predictors goes to infinity. Under regularity conditions we also achieve the asymptotic normality when the dimension of predictor vector goes to infinity at the rate of pn = o (n1 / 3) where n is sample size, which enables us to construct confidence interval/region for the estimated index. The asymptotic results are augmented by simulations, and illustrated by analysis of an air pollution dataset. © 2008 Elsevier Inc. All rights reserved.

Keywords

62G20, 62H15, Dimension reduction, Diverging parameters, Inverse regression, SCAD, Sparsity

Publication Date

2009

Source Publication Title

Journal of Multivariate Analysis

Volume

100

Issue

5

Start Page

862

End Page

875

Publisher

Elservier

DOI

10.1016/j.jmva.2008.09.003

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.jmva.2008.09.003

ISSN (print)

0047259X

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