Title

Improving dimension reduction via contour-projection

Authors

Authors

H. S. Wang; L. Q. Ni;C. L. Tsai

Comments

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Abbreviated Journal Title

Stat. Sin.

Keywords

contour-projection; dimension reduction; linearity condition; sliced; average variance estimation; sliced inverse regression; SLICED INVERSE REGRESSION; DISTRIBUTIONS; Statistics & Probability

Abstract

Most sufficient dimension reduction methods hinge on the existence of finite moments of the predictor vector, a characteristic which is not necessarily warranted for every elliptically contoured distribution as commonly encountered in practice. Hence, we propose a contour-projection approach, which projects the elliptically distributed predictor vector onto a unit contour, which shares the same shape as the predictor density contour. As a result, the projected vector has finite moments of any order. Furthermore, contour-projection yields a hybrid predictor vector, which encompasses both the direction and length of the original predictor vector. Therefore, it naturally leads to a substantial improvement on many existing dimension reduction methods (e.g., sliced inverse regression and sliced average variance estimation) when the predictor vector has a heavy-tailed distribution. Numerical studies confirm our theoretical findings.

Journal Title

Statistica Sinica

Volume

18

Issue/Number

1

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

299

Last Page

311

WOS Identifier

WOS:000253098700028

ISSN

1017-0405

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