INTERACTION SPLINE MODELS AND THEIR CONVERGENCE-RATES

• 成果类型: Article
• 署名作者: CHEN, ZH
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348374
• 发表日期: 1991
• 页码: 1855-1868
• 关键词: linear smoothers; ADDITIVE-MODELS; regression

摘要

We consider interaction splines which model a multivariate regression function f as a constant plus the sum of functions of one variable (main effects), plus the sum of functions of two variables (two-factor interactions), and so on. The estimation of f by the penalized least squares method and the asymptotic properties of the models are studied in this article. It is shown that, under some regularity conditions on the data points, the expected squared error averaged over the data points converges to zero at a rate of O(N-2m/(2m+1)) as the sample size N --> infinity if the smoothing parameters are appropriately chosen, where m is a measure of the assumed smoothness of f.