Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Partial linear single index models with distortion measurement errors

Language

English

Abstract

We study partial linear single index models when the response and the covariates in the parametric part are measured with errors and distorted by unknown functions of commonly observable confounding variables, and propose a semiparametric covariate-adjusted estimation procedure. We apply the minimum average variance estimation method to estimate the parameters of interest. This is different from all existing covariate-adjusted methods in the literature. Asymptotic properties of the proposed estimators are established. Moreover, we also study variable selection by adopting the coordinate-independent sparse estimation to select all relevant but distorted covariates in the parametric part. We show that the resulting sparse estimators can exclude all irrelevant covariates with probability approaching one. A simulation study is conducted to evaluate the performance of the proposed methods and a real data set is analyzed for illustration. © 2012 The Institute of Statistical Mathematics, Tokyo.

Keywords

Coordinate-independent sparse estimation (CISE), Covariate adjusted, Dimension reduction, Distorting function, Measurement errors, Minimum average variance estimation (MAVE), Single index, Sparse principle component (SPC)

Publication Date

2013

Source Publication Title

Annals of the Institute of Statistical Mathematics

Volume

65

Issue

2

Start Page

237

End Page

267

Publisher

Springer

DOI

10.1007/s10463-012-0371-z

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10463-012-0371-z

ISSN (print)

00203157

ISSN (electronic)

15729052

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