Dimension reduction in regression without matrix inversion

• 成果类型: Article
• 署名作者: Cook, Dennis; Li, Bing; Chiaromonte, Francesca
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asm038
• 发表日期: 2007
• 页码: 569584
• 关键词: alignments

摘要

Regressions in which the fixed number of predictors p exceeds the number of independent observational units n occur in a variety of scientific fields. Sufficient dimension reduction provides a promising approach to such problems, by restricting attention to d < n linear combinations of the original p predictors. However, standard methods of sufficient dimension reduction require inversion of the sample predictor covariance matrix. We propose a method for estimating the central subspace that eliminates the need for such inversion and is applicable regardless of the ( n, p) relationship. Simulations show that our method compares favourably with standard large sample techniques when the latter are applicable. We illustrate our method with a genomics application.