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December 2007 A constructive approach to the estimation of dimension reduction directions
Yingcun Xia
Ann. Statist. 35(6): 2654-2690 (December 2007). DOI: 10.1214/009053607000000352

Abstract

In this paper we propose two new methods to estimate the dimension-reduction directions of the central subspace (CS) by constructing a regression model such that the directions are all captured in the regression mean. Compared with the inverse regression estimation methods [e.g., J. Amer. Statist. Assoc. 86 (1991) 328–332, J. Amer. Statist. Assoc. 86 (1991) 316–342, J. Amer. Statist. Assoc. 87 (1992) 1025–1039], the new methods require no strong assumptions on the design of covariates or the functional relation between regressors and the response variable, and have better performance than the inverse regression estimation methods for finite samples. Compared with the direct regression estimation methods [e.g., J. Amer. Statist. Assoc. 84 (1989) 986–995, Ann. Statist. 29 (2001) 1537–1566, J. R. Stat. Soc. Ser. B Stat. Methodol. 64 (2002) 363–410], which can only estimate the directions of CS in the regression mean, the new methods can detect the directions of CS exhaustively. Consistency of the estimators and the convergence of corresponding algorithms are proved.

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Yingcun Xia. "A constructive approach to the estimation of dimension reduction directions." Ann. Statist. 35 (6) 2654 - 2690, December 2007. https://doi.org/10.1214/009053607000000352

Information

Published: December 2007
First available in Project Euclid: 22 January 2008

zbMATH: 1360.62196
MathSciNet: MR2382662
Digital Object Identifier: 10.1214/009053607000000352

Subjects:
Primary: 62G08
Secondary: 62G09 , 62H05

Keywords: Conditional density function , convergence of algorithm , double-kernel smoothing , efficient dimension reduction , root-n consistency

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 6 • December 2007
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