## The Annals of Statistics

### 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.

#### Article information

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

Dates
First available in Project Euclid: 7 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.aos/1407420012

Digital Object Identifier
doi:10.1214/14-AOS1242

Mathematical Reviews number (MathSciNet)
MR3262464

Zentralblatt MATH identifier
1310.62052

Subjects
Primary: 62J07: Ridge regression; shrinkage estimators

#### Citation

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. https://projecteuclid.org/euclid.aos/1407420012

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