Smoothing parameter selection for a class of semiparametric linear models

• 成果类型: Article
• 署名作者: Reiss, Philip T.; Ogden, R. Todd
• 署名单位: New York University; Nathan Kline Institute for Psychiatric Research; Columbia University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2008.00695.x
• 发表日期: 2009
• 页码: 505-523
• 关键词: regression; splines; component; tests

摘要

Spline-based approaches to non-parametric and semiparametric regression, as well as to regression of scalar outcomes on functional predictors, entail choosing a parameter controlling the extent to which roughness of the fitted function is penalized. We demonstrate that the equations determining two popular methods for smoothing parameter selection, generalized cross-validation and restricted maximum likelihood, share a similar form that allows us to prove several results which are common to both, and to derive a condition under which they yield identical values. These ideas are illustrated by application of functional principal component regression, a method for regressing scalars on functions, to two chemometric data sets.