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arXiv · 1408.3221

An adaptive composite quantile approach to dimension reduction

Efang Kong·Yingcun Xia
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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.

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Efang Kong, Yingcun Xia. 2014-08-14. An adaptive composite quantile approach to dimension reduction. https://doi.org/10.1214/14-aos1242

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