A COMPARISON OF A SPLINE ESTIMATE TO ITS EQUIVALENT KERNEL ESTIMATE

• 成果类型: Article
• 署名作者: MESSER, K
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348122
• 发表日期: 1991
• 页码: 817-829
• 关键词: regression

摘要

It has been observed that to a smoothing spline operator there corresponds an equivalent kernel operator; these two operators have been compared in a variety of norms [Cox (1984), Silverman (1984)]. In this paper, we refine the existing bounds for the particular case of the spline estimator considered in Rice and Rosenblatt (1983) and its corresponding equivalent kernel estimator. We obtain detailed asymptotic expressions for the bias and covariance functions of the two estimates and provide rates of convergence. Direct comparison then shows that the two estimates are similar. They may differ somewhat in their higher order boundary behavior.