ESTIMATING SUFFICIENT REDUCTIONS OF THE PREDICTORS IN ABUNDANT HIGH-DIMENSIONAL REGRESSIONS

• 成果类型: Article
• 署名作者: Cook, R. Dennis; Forzani, Liliana; Rothman, Adam J.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); National University of the Littoral
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS962
• 发表日期: 2012
• 页码: 353-384
• 关键词: sliced inverse regression; COVARIANCE ESTIMATION; components; matrices; MODEL

摘要

We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are consistent in a variety of settings, particularly in abundant regressions where most predictors contribute some information on the response, and oracle rates are possible. Simulation results are presented to support the theoretical conclusion.