Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

On splines approximation for sliced average variance estimation

Language

English

Abstract

To avoid the inconsistency and slow convergence rate of the slicing estimator of the sliced average variance estimation (SAVE), particularly in the continuous response cases, we suggest B-spline approximation that can make the estimator sqrt(n) consistent and keeps the spirit of easy implementation that the slicing estimation shares. Compared with kernel estimation that has been used in the literature, B-spline approximation is of higher accuracy and is easier to implement. To estimate the structural dimension of the central dimension reduction space, a modified Bayes information criterion is suggested, which makes the leading term and the penalty term comparable in magnitude. This modified criterion can help to enhance the efficacy of estimation. The methodologies and theoretical results are illustrated through an application to the horse mussel data and simulation comparisons with existing methods by simulations. © 2008 Elsevier B.V. All rights reserved.

Keywords

Asymptotic normality, B-spline, Bayes information criterion, Dimension reduction, Sliced average variance estimation, Structural dimension

Publication Date

2009

Source Publication Title

Journal of Statistical Planning and Inference

Volume

139

Issue

4

Start Page

1493

End Page

1505

Publisher

Elservier

DOI

10.1016/j.jspi.2008.07.017

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.jspi.2008.07.017

ISSN (print)

03783758

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