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