http://dx.doi.org/10.1093/biomet/asq018">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Sufficient dimension reduction through discretization-expectation estimation

Language

English

Abstract

In the context of sufficient dimension reduction, the goal is to parsimoniously recover the central subspace of a regression model. Many inverse regression methods use slicing estimation to recover the central subspace. The efficacy of slicing estimation depends heavily upon the number of slices. However, the selection of the number of slices is an open and long-standing problem. In this paper, we propose a discretization-expectation estimation method, which avoids selecting the number of slices, while preserving the integrity of the central subspace. This generic method assures root-n consistency and asymptotic normality of slicing estimators for many inverse regression methods, and can be applied to regressions with multivariate responses. A BIC-type criterion for the dimension of the central subspace is proposed. Comprehensive simulations and an illustrative application show that our method compares favourably with existing estimators. © 2010 Biometrika Trust.

Keywords

Binary response, Central subspace, Dimension reduction, Graphical regression, Sliced inverse regression

Publication Date

2010

Source Publication Title

Biometrika

Volume

97

Issue

2

Start Page

295

End Page

304

Publisher

Oxford University Press

ISSN (print)

00063444

ISSN (electronic)

14643510

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