Sufficient dimension reduction via inverse regression: A minimum discrepancy approach

• 成果类型: Article
• 署名作者: Cook, RD; Ni, LQ
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; State University System of Florida; University of Central Florida
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000001501
• 发表日期: 2005
• 页码: 410-428
• 关键词: principal hessian directions; least-squares; structural dimension; ASYMPTOTIC THEORY; Visualization; algorithms

摘要

A family of dimension-reduction methods, the inverse regression (IR) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspace is asymptotically efficient, (2) its test statistic for dimension has an asymptotic chi-squared distribution, and (3) it provides a chi-squared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors. Current methods like sliced inverse regression belong to a suboptimal class of the IR family. Comparisons of these methods are reported through simulation studies. The approach developed here also allows a relatively straightforward derivation of the asymptotic null distribution of the test statistic for dimension used in sliced average variance estimation.