Risk bounds in isotonic regression

被引：71
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.
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收藏
页码：528 / 555
页数：28
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