Partial least squares regression on smooth factors

• 成果类型: Article
• 署名作者: Goutis, C; Fearn, T
• 署名单位: University of London; University College London
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2291658
• 发表日期: 1996
• 页码: 627-632
• 关键词: Calibration; selection

摘要

In this article we present a modification of partial least squares regression to account for inherent nonexchangeabilities of the columns of the design matrix. In chemometrics applications it is common to write the matrix as a bilinear form of latent variables and loadings. These loadings are often interpreted as sampled values of functions; hence they should exhibit a degree of smoothness. Our method forces the partial least squares factors to be smooth, by using a roughness penalty motivated by nonparametric regression. We present a computational method to determine the loadings that guarantees a desired orthogonality at successive steps. We propose a cross-validatory choice of the smoothing parameter and the number of loadings. We illustrate the algorithm by an example and describe our experience with real data.