RATES OF CONVERGENCE FOR THE ESTIMATES OF THE OPTIMAL TRANSFORMATIONS OF VARIABLES

• 成果类型: Article
• 署名作者: BURMAN, P
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348116
• 发表日期: 1991
• 页码: 702-723
• 关键词: generalized additive-models; regression

摘要

We consider here spline estimates of the optimal transformations of variables for multiple correlation and regression as dealt with in a recent paper by Breiman and friedman. We show that we can construct estimates of the optimal transformations which have the same optimal rate of convergence as in the usual nonparametric estimation of a univariate function.