Risk bounds in isotonic regression

被引：69
|
作者：
Zhang, CH [1 ]
机构：
[1] Rutgers State Univ, Hill Ctr, Dept Stat, Piscataway, NJ 08854 USA
来源：
ANNALS OF STATISTICS | 2002年 / 30卷 / 02期
关键词：
nonparametric regression; isotonic regression; risk bounds; least squares estimator; maximum likelihood estimator;
D O I：
10.1214/aos/1021379864
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：
Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal Lip to scale constants. and they imply uniform n(-1/3)-consistency of the l(p) risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability distribution of the data, with possibly dependent observations.
引用
收藏
页码：528 / 555
页数：28
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