# AN ADAPTIVE COMPOSITE QUANTILE APPROACH TO DIMENSION REDUCTION

Kong, Efang (2014) AN ADAPTIVE COMPOSITE QUANTILE APPROACH TO DIMENSION REDUCTION. Annals of Statistics, 42 (4). pp. 1657-1688. ISSN 0090-5364. (doi:10.1214/14-AOS1242)

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## Abstract

Sufficient dimension reduction [Li 1991] 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.

Item Type: Article 10.1214/14-AOS1242 Bahadur approximation; sufficient dimension reduction; local polynomial smoothing; quantile regression; semiparametric models; U-processes Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics Efang Kong 29 May 2014 13:44 UTC 21 Jan 2020 09:44 UTC https://kar.kent.ac.uk/id/eprint/41213 (The current URI for this page, for reference purposes)