Contour projected dimension reduction
Ronghua Luo, Hansheng Wang, and Chih-Ling Tsai
Source: Ann. Statist. Volume 37, Number 6B (2009), 3743-3778.
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 [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.
Primary Subjects: 62G08
Secondary Subjects: 62G35, 62G20
Keywords: Central subspace; central contour subspace; contour projection; directional regression; generalized contour subspace; kernel contour subspace; $\sqrt{n}$-consistency; sliced average variance estimation; sliced inverse regression; sufficient contour subspace
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1256303526
Digital Object Identifier: doi:10.1214/08-AOS679
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