CONTOUR PROJECTED DIMENSION REDUCTION

• 成果类型: Article
• 署名作者: Luo, Ronghua; Wang, Hansheng; Tsai, Chih-Ling
• 署名单位: Southwestern University of Finance & Economics - China; Peking University; University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS679
• 发表日期: 2009
• 页码: 3743-3778
• 关键词: principal hessian directions; inverse regression; asymptotics

摘要

In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their structural dimensions are no larger than that of the central subspace Cook [Regression Graphics (1998b) Wiley]. Furthermore, we employ CP-sliced inverse regression, CP-sliced average variance estimation and CP-directional regression to estimate the generalized contour,subspace, and we subsequently obtain their theoretical properties. Monte Carlo studies demonstrate that the three CP-based dimension reduction methods outperform their corresponding non-CP approaches when the predictors have heavy-tailed elliptical distributions. An empirical example is also presented to illustrate the usefulness of the CP method.