PARTIAL LEAST SQUARES PREDICTION IN HIGH-DIMENSIONAL REGRESSION

• 成果类型: Article
• 署名作者: Cook, R. Dennis; Forzani, Liliana
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; National University of the Littoral
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1681
• 发表日期: 2019
• 页码: 884-908
• 关键词: infrared spectroscopy; reduction; CLASSIFICATION

摘要

We study the asymptotic behavior of predictions from partial least squares (PLS) regression as the sample size and number of predictors diverge in various alignments. We show that there is a range of regression scenarios where PLS predictions have the usual root-n convergence rate, even when the sample size is substantially smaller than the number of predictors, and an even wider range where the rate is slower but may still produce practically useful results. We show also that PLS predictions achieve their best asymptotic behavior in abundant regressions where many predictors contribute information about the response. Their asymptotic behavior tends to be undesirable in sparse regressions where few predictors contribute information about the response.