Some insights into continuum regression and its asymptotic properties

• 成果类型: Article
• 署名作者: Chen, Xin; Cook, R. Dennis
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq024
• 发表日期: 2010
• 页码: 985989
• 关键词: partial least-squares; Dimension Reduction; components

摘要

Continuum regression encompasses ordinary least squares regression, partial least squares regression and principal component regression under the same umbrella using a nonnegative parameter gamma. However, there seems to be no literature discussing the asymptotic properties for arbitrary continuum regression parameter gamma. This article establishes a relation between continuum regression and sufficient dimension reduction and studies the asymptotic properties of continuum regression for arbitrary gamma under inverse regression models. Theoretical and simulation results show that the continuum seems unnecessary when the conditional distribution of the predictors given the response follows the multivariate normal distribution.