Nearest neighbor inverse regression

• 成果类型: Article
• 署名作者: Hsing, T
• 署名单位: National University of Singapore; Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1018031213
• 发表日期: 1999
• 页码: 697-731
• 关键词: projection pursuit regression; principal hessian directions; Dimension Reduction

摘要

Sliced inverse regression (SIR), formally introduced by Li, is a very general procedure for performing dimension reduction in nonparametric regression. This paper considers a version of SIR in which the slices are determined by nearest neighbors and the response variable takes value possibly in a multidimensional space. It is shown, under general conditions, that the effective dimension reduction space can be estimated with rate n(-1/2) where n is the sample size.