An adaptive composite quantile approach to dimension reduction

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.

Published in at http://dx.doi.org/10.1214/14-AOS1242 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Composite quantile regression and the oracle Model Selection Theory
• Kernel dimension reduction in regression
• Fisher Lecture: Dimension Reduction in Regression
• Sufficient dimension reduction based on an ensemble of minimum average variance estimators