Open Access
June 2009 Dimension reduction for nonelliptically distributed predictors
Bing Li, Yuexiao Dong
Ann. Statist. 37(3): 1272-1298 (June 2009). DOI: 10.1214/08-AOS598


Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately. For example, a typical dimension reduction method would require the predictor to have elliptical or even multivariate normal distribution. In this paper, we reformulate the commonly used dimension reduction methods, via the notion of “central solution space,” so as to circumvent the requirements of such strong assumptions, while at the same time preserve the desirable properties of the classical methods, such as $\sqrt{n}$-consistency and asymptotic normality. Imposing elliptical distributions or even stronger assumptions on predictors is often considered as the necessary tradeoff for overcoming the “curse of dimensionality,” but the development of this paper shows that this need not be the case. The new methods will be compared with existing methods by simulation and applied to a data set.


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Bing Li. Yuexiao Dong. "Dimension reduction for nonelliptically distributed predictors." Ann. Statist. 37 (3) 1272 - 1298, June 2009.


Published: June 2009
First available in Project Euclid: 10 April 2009

zbMATH: 1160.62050
MathSciNet: MR2509074
Digital Object Identifier: 10.1214/08-AOS598

Primary: 62G08 , 62G09 , 62H12

Keywords: Canonical correlation , central solution spaces , inverse regression , kernel inverse regression , parametric inverse regression , sliced inverse regression

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 3 • June 2009
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