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
相关论文
共 50 条
  • [11] Bounded isotonic regression
    Luss, Ronny
    Rosset, Saharon
    ELECTRONIC JOURNAL OF STATISTICS, 2017, 11 (02): : 4488 - 4514
  • [12] AN ISOTONIC REGRESSION ALGORITHM
    DYKSTRA, RL
    JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1981, 5 (04) : 355 - 363
  • [13] The bias of isotonic regression
    Dai, Ran
    Song, Hyebin
    Barber, Rina Foygel
    Raskutti, Garvesh
    ELECTRONIC JOURNAL OF STATISTICS, 2020, 14 (01): : 801 - 834
  • [14] Causal isotonic regression
    Westling, Ted
    Gilbert, Peter
    Carone, Marco
    JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2020, 82 (03) : 719 - 747
  • [15] Generalized Isotonic Regression
    Luss, Ronny
    Rosset, Saharon
    JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, 2014, 23 (01) : 192 - 210
  • [16] Isotonic distributional regression
    Henzi, Alexander
    Ziegel, Johanna F.
    Gneiting, Tilmann
    JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2021, 83 (05) : 963 - 993
  • [17] Private Isotonic Regression
    Ghazi, Badih
    Kamath, Pritish
    Kumar, Ravi
    Manurangsi, Pasin
    ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 35, NEURIPS 2022, 2022,
  • [18] Adaptive quantile regression with precise risk bounds
    TIAN MaoZai
    CHAN Ngai Hang
    ScienceChina(Mathematics), 2017, 60 (05) : 875 - 896
  • [19] Adaptive quantile regression with precise risk bounds
    Tian, MaoZai
    Chan, Ngai Hang
    SCIENCE CHINA-MATHEMATICS, 2017, 60 (05) : 875 - 896
  • [20] Adaptive quantile regression with precise risk bounds
    MaoZai Tian
    Ngai Hang Chan
    Science China Mathematics, 2017, 60 : 875 - 896
12345