Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions

• 成果类型: Article
• 署名作者: Horowitz, Joel L.; Mammen, Enno
• 署名单位: Northwestern University; University of Mannheim
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000415
• 发表日期: 2007
• 页码: 2589-2619
• 关键词: additive-models; linear-models; likelihood estimation; asymptotic properties; splines; series

摘要

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion.