Open Access
December 2009 Contour projected dimension reduction
Ronghua Luo, Hansheng Wang, Chih-Ling Tsai
Ann. Statist. 37(6B): 3743-3778 (December 2009). DOI: 10.1214/08-AOS679


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 [Regression Graphics (1998b) Wiley]. 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.


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Ronghua Luo. Hansheng Wang. Chih-Ling Tsai. "Contour projected dimension reduction." Ann. Statist. 37 (6B) 3743 - 3778, December 2009.


Published: December 2009
First available in Project Euclid: 23 October 2009

zbMATH: 1360.62184
MathSciNet: MR2572442
Digital Object Identifier: 10.1214/08-AOS679

Primary: 62G08
Secondary: 62G20 , 62G35

Keywords: $\sqrt{n}$-consistency , central contour subspace , central subspace , contour projection , directional regression , generalized contour subspace , kernel contour subspace , sliced average variance estimation , sliced inverse regression , sufficient contour subspace

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6B • December 2009
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