Consistency for the least squares estimator in nonparametric regression
成果类型：
Article
署名作者：
VandeGeer, S; Wegkamp, M
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1996
页码：
2513-2523
关键词：
摘要：
We shall study the general regression model Y = g(0)(X) + epsilon, where X and epsilon are independent. The available information about g(0) can be expressed by g(0) is an element of G for some class G. As an estimator of g(0) we choose the least squares estimator. We shall give necessary and sufficient conditions for consistency of this estimator in terms of(basically) geometric properties of G. Our main tool will be the theory of empirical processes.