The Annals of Statistics

An adaptive composite quantile approach to dimension reduction

Efang Kong and Yingcun Xia

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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.

Article information

Ann. Statist., Volume 42, Number 4 (2014), 1657-1688.

First available in Project Euclid: 7 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J07: Ridge regression; shrinkage estimators

Bahadur approximation sufficient dimension reduction local polynomial smoothing quantile regression semiparametric models U-processes


Kong, Efang; Xia, Yingcun. An adaptive composite quantile approach to dimension reduction. Ann. Statist. 42 (2014), no. 4, 1657--1688. doi:10.1214/14-AOS1242.

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