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August 2005 Contour regression: A general approach to dimension reduction
Bing Li, Hongyuan Zha, Francesca Chiaromonte
Ann. Statist. 33(4): 1580-1616 (August 2005). DOI: 10.1214/009053605000000192


We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response, leading to simple and general contour regression (SCR and GCR) methodology. In comparison with existing sufficient dimension reduction techniques, this contour-based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions, while maintaining $\sqrt{n}$-consistency and computational ease. Moreover, it proves robust to departures from ellipticity. We establish population properties for both SCR and GCR, and asymptotic properties for SCR. Simulations to compare performance with that of standard techniques such as ordinary least squares, sliced inverse regression, principal Hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses. We demonstrate the use of contour-based methods on a data set concerning soil evaporation.


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Bing Li. Hongyuan Zha. Francesca Chiaromonte. "Contour regression: A general approach to dimension reduction." Ann. Statist. 33 (4) 1580 - 1616, August 2005.


Published: August 2005
First available in Project Euclid: 5 August 2005

zbMATH: 1078.62033
MathSciNet: MR2166556
Digital Object Identifier: 10.1214/009053605000000192

Primary: 62G08
Secondary: 62G09 , 62H05

Keywords: central subspace , data visualization , empirical directions , Nonparametric regression , PCA

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 4 • August 2005
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