AN RKHS FORMULATION OF THE INVERSE REGRESSION DIMENSION-REDUCTION PROBLEM

• 成果类型: Article
• 署名作者: Hsing, Tailen; Ren, Haobo
• 署名单位: University of Michigan System; University of Michigan; Sanofi-Aventis; Sanofi USA
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS589
• 发表日期: 2009
• 页码: 726-755
• 关键词: sample paths; principal

摘要

Suppose that Y is a scalar and X is a second-order stochastic process, where Y and X are conditionally independent given the random variables xi(1), ..., xi(p) which belong to the closed span L-X(2) of X. This paper investigates a unified framework for the inverse regression dimension-reduction problem. It is found that the identification of L-X(2) with the reproducing kernel Hilbert space of X provides a platform for a seamless extension from the finite- to infinite-dimensional settings. It also facilitates convenient computational algorithms that can be applied to a variety of models.