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August 2014 An adaptive composite quantile approach to dimension reduction
Efang Kong, Yingcun Xia
Ann. Statist. 42(4): 1657-1688 (August 2014). DOI: 10.1214/14-AOS1242

Abstract

Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316–342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an adaptive composite quantile approach. Compared to existing methods, (1) it requires minimal assumptions and is capable of revealing all dimension reduction directions; (2) it is robust against outliers and (3) it is structure-adaptive, thus more efficient. Asymptotic results are proved and numerical examples are provided, including a real data analysis.

Citation

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Efang Kong. Yingcun Xia. "An adaptive composite quantile approach to dimension reduction." Ann. Statist. 42 (4) 1657 - 1688, August 2014. https://doi.org/10.1214/14-AOS1242

Information

Published: August 2014
First available in Project Euclid: 7 August 2014

zbMATH: 1310.62052
MathSciNet: MR3262464
Digital Object Identifier: 10.1214/14-AOS1242

Subjects:
Primary: 62J07

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 4 • August 2014
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