Contour Projected Dimension Reduction

The Annals of Statistics, Forthcoming

52 Pages Posted: 24 Dec 2008

See all articles by Ronghua Luo

Ronghua Luo

Southwestern University of Finance and Economics (SWUFE) - School of Finance

Hansheng Wang

Peking University - Guanghua School of Management

Chih-Ling Tsai

University of California, Davis - Graduate School of Management

Date Written: December 22, 2008

Abstract

In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their structural dimensions are no larger than that of the central subspace (Cook, 1998b). Furthermore, we employ CP-sliced inverse regression, CP-sliced average variance estimation, and CP-directional regression to estimate the generalized contour subspace, and we subsequently obtain their theoretical properties. Monte Carlo studies demonstrate that the three CP-based dimension reduction methods outperform their corresponding non-CP approaches, when the predictors have heavy-tailed elliptical distributions. An empirical example is also presented to illustrate the usefulness of the CP method.

Keywords: central subspace, central contour subspace, contour projection, directional regression, generalized contour subspace

Suggested Citation

Luo, Ronghua and Wang, Hansheng and Tsai, Chih-Ling, Contour Projected Dimension Reduction (December 22, 2008). The Annals of Statistics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1319598

Ronghua Luo

Southwestern University of Finance and Economics (SWUFE) - School of Finance ( email )

Chengdu, 610074
China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Chih-Ling Tsai

University of California, Davis - Graduate School of Management ( email )

One Shields Avenue
Davis, CA 95616
United States

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