Consistency for the least squares estimator in nonparametric regression

被引：0
|
作者：
VandeGeer, S
Wegkamp, M
机构：
来源：
ANNALS OF STATISTICS | 1996年 / 24卷 / 06期
关键词：
consistency; empirical process; entropy; Glivenko-Cantelli classes; least squares estimation; regression;
D O I：
暂无
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：2513 / 2523
页数：11
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