Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

A data adaptive hybrid method for dimension reduction

Language

English

Abstract

To gain the advantages of different inverse regression methods, the convex combination can be useful for estimating the central subspace. To select an appropriate combination coefficient in the hybrid method, we propose in this paper a data-adaptive hybrid method using the trace of kernel matrices. For ease of illustration, we consider particularly the combination of inverse regressions using the conditional mean and the conditional variance, both of which are separately powerful in estimating different models. Because the efficacy of the slicing estimation may deteriorate when it is used to estimate the conditional variance, we use the kernel smoother instead. The asymptotic normality at the root-n rate is achieved even with the data-driven combination weight. Illustrative examples by simulations and an application to horse mussel data is presented to demonstrate the necessity of the hybrid models and the efficacy of our kernel estimation. © 2009 Taylor & Francis.

Keywords

Asymptotic normality, Central subspace, Dimension reduction, Inverse regression

Publication Date

2009

Source Publication Title

Journal of Nonparametric Statistics

Volume

21

Issue

7

Start Page

851

End Page

861

Publisher

American Statistical Association

DOI

10.1080/10485250902980568

Link to Publisher's Edition

http://dx.doi.org/10.1080/10485250902980568

ISSN (print)

10485252

ISSN (electronic)

10290311

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