文章基本信息

标题：Principal quantile regression for sufficient dimension reduction with heteroscedasticity
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作者：Chong Wang ; Seung Jun Shin ; Yichao Wu 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2018
卷号：12
期号：2
页码：2114-2140
DOI：10.1214/18-EJS1432
语种：English
出版社：Institute of Mathematical Statistics
摘要：Sufficient dimension reduction (SDR) is a successful tool for reducing data dimensionality without stringent model assumptions. In practice, data often display heteroscedasticity which is of scientific importance in general but frequently overlooked since a primal goal of most existing statistical methods is to identify conditional mean relationship among variables. In this article, we propose a new SDR method called principal quantile regression (PQR) that efficiently tackles heteroscedasticity. PQR can naturally be extended to a nonlinear version via kernel trick. Asymptotic properties are established and an efficient solution path-based algorithm is provided. Numerical examples based on both simulated and real data demonstrate the PQR’s advantageous performance over existing SDR methods. PQR still performs very competitively even for the case without heteroscedasticity.