A unified framework for spline estimators

• 成果类型: Article
• 署名作者: Schwarz, Katsiaryna; Krivobokova, Tatyana
• 署名单位: University of Gottingen
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv070
• 发表日期: 2016
• 页码: 121131
• 关键词: Asymptotics; Kernels

摘要

This article develops a unified framework to study the asymptotic properties of all periodic spline-based estimators, that is, of regression, penalized and smoothing splines. The explicit form of the periodic Demmler-Reinsch basis in terms of exponential splines allows the derivation of an expression for the asymptotic equivalent kernel on the real line for all spline estimators simultaneously. The corresponding bandwidth, which drives the asymptotic behaviour of spline estimators, is shown to be a function of the number of knots and the smoothing parameter. Strategies for the selection of the optimal bandwidth and other model parameters are discussed.