From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression

• 成果类型: Article
• 署名作者: Kou, SC
• 署名单位: Harvard University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000841
• 发表日期: 2004
• 页码: 2444-2468
• 关键词: smoothing parameter selection; generalized cross-validation; maximum-likelihood; EFFICIENCY; optimality; cl

摘要

This paper studies, under the setting of spline regression, the connection between finite-sample properties of selection criteria and their asymptotic counterparts, focusing on bridging the gap between the two. We introduce a bias-variance decomposition of the prediction error, using which it is shown that in the asymptotics the bias term dominates the variability term, providing an explanation of the gap. A geometric exposition is provided for intuitive understanding. The theoretical and geometric results are illustrated through a numerical example.