AN ADAPTIVE COMPOSITE QUANTILE APPROACH TO DIMENSION REDUCTION

• 成果类型: Article
• 署名作者: Kong, Efang; Xia, Yingcun
• 署名单位: University of Kent; National University of Singapore
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1242
• 发表日期: 2014
• 页码: 1657-1688
• 关键词: central subspace; regression; kernel; asymptotics; variance

摘要

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.