Variance estimation in nonparametric multiple regression

被引：7
|
作者：
Kulasekera, KB
Gallagher, C
机构：
[1] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA
[2] Calif State Univ Los Angeles, Dept Math & Stat, Chico, CA 95929 USA
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2002年 / 31卷 / 08期
关键词：
nonparametric regression surface; difference method; asymptotic distribution; sparse design;
D O I：
10.1081/STA-120006074
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 consider the variance estimation in a general nonparametric regression model with multiple covariates. We extend difference methods to the multivariate setting by introducing an algorithm that orders the design points in higher dimensions. We also consider an adaptive difference estimator which requires much less strict assumptions on the covariate design and can significantly reduce mean squared error for small sample sizes.
引用
收藏
页码：1373 / 1383
页数：11
相关论文
共 50 条
  • [1] THE ESTIMATION OF RESIDUAL VARIANCE IN NONPARAMETRIC REGRESSION
    BUCKLEY, MJ
    EAGLESON, GK
    SILVERMAN, BW
    [J]. BIOMETRIKA, 1988, 75 (02) : 189 - 199
  • [2] On conditional variance estimation in nonparametric regression
    Chib, Siddhartha
    Greenberg, Edward
    [J]. STATISTICS AND COMPUTING, 2013, 23 (02) : 261 - 270
  • [3] ON VARIANCE-ESTIMATION IN NONPARAMETRIC REGRESSION
    HALL, P
    MARRON, JS
    [J]. BIOMETRIKA, 1990, 77 (02) : 415 - 419
  • [4] On conditional variance estimation in nonparametric regression
    Siddhartha Chib
    Edward Greenberg
    [J]. Statistics and Computing, 2013, 23 : 261 - 270
  • [5] On the estimation of a monotone conditional variance in nonparametric regression
    Dette, Holger
    Pilz, Kay
    [J]. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2009, 61 (01) : 111 - 141
  • [6] On the estimation of a monotone conditional variance in nonparametric regression
    Holger Dette
    Kay Pilz
    [J]. Annals of the Institute of Statistical Mathematics, 2009, 61 : 111 - 141
  • [7] Variance estimation in nonparametric regression with jump discontinuities
    Dai, Wenlin
    Tong, Tiejun
    [J]. JOURNAL OF APPLIED STATISTICS, 2014, 41 (03) : 530 - 545
  • [8] ADAPTIVE VARIANCE FUNCTION ESTIMATION IN HETEROSCEDASTIC NONPARAMETRIC REGRESSION
    Cai, T. Tony
    Wang, Lie
    [J]. ANNALS OF STATISTICS, 2008, 36 (05): : 2025 - 2054
  • [9] Effect of mean on variance function estimation in nonparametric regression
    Wang, Lie
    Brown, Lawrence D.
    Cai, T. Tony
    Levine, Michael
    [J]. ANNALS OF STATISTICS, 2008, 36 (02): : 646 - 664
  • [10] Estimation and inference for error variance in bivariate nonparametric regression
    Bock, M.
    Bowman, A. W.
    Ismail, B.
    [J]. STATISTICS AND COMPUTING, 2007, 17 (01) : 39 - 47
12345