Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Estimation of a groupwise additive multiple-index model and its applications

Language

English

Abstract

In this paper, we propose a simple linear least squares framework to deal with estimation and selection for a groupwise additive multiple-index model, of which the partially linear single-index model is a special case, and in which each component function has a single-index structure. We show that, somewhat unexpectedly, all index vectors can be recovered through a single least squares coefficient vector. As a direct application, for partially linear single-index models we develop a new two-stage estimation procedure that is iterative-free and easily implemented. This estimation approach can also be applied to develop, for the semi-parametric model under study, a penalized least squares estimation and establish its asymptotic behavior in sparse and high-dimensional settings without any nonparametric treatment. A simulation study and a data analysis are presented.

Keywords

High dimensionality, Index estimation, Least squares, Multipleindex models, Variable selection

Publication Date

2015

Source Publication Title

Statistica Sinica

Volume

25

Issue

2

Start Page

551

End Page

566

Publisher

Academia Sinica, Institute of Statistical Science

DOI

10.5705/ss.2013.175

Link to Publisher's Edition

http://dx.doi.org/10.5705/ss.2013.175

ISSN (print)

10170405

ISSN (electronic)

19968507

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