METHODOLOGY AND THEORY FOR PARTIAL LEAST SQUARES APPLIED TO FUNCTIONAL DATA

• 成果类型: Article
• 署名作者: Delaigle, Aurore; Hall, Peter
• 署名单位: University of Melbourne; University of California System; University of California Davis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS958
• 发表日期: 2012
• 页码: 322-352
• 关键词: pls regression; CLASSIFICATION; prediction

摘要

The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares estimator of slope is either used to construct linear predictive models, or as a tool to project the data onto a one-dimensional quantity that is employed for further statistical analysis. Although the partial least squares approach is often viewed as an attractive alternative to projections onto the principal component basis, its properties are less well known than those of the latter, mainly because of its iterative nature. We develop an explicit formulation of Partial least squares for functional data, which leads to insightful results and Motivates new theory, demonstrating consistency and establishing convergence rates.