ADAPTIVE ESTIMATION IN A HETEROSCEDASTIC NONPARAMETRIC REGRESSION

被引：2
|
作者：
Pchelintsev, E. A. [1 ]
Perelevskiy, S. S. [1 ]
机构：
[1] Tomsk State Univ, Tomsk, Russia
来源：
VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS | 2019年 / 57期
关键词：
heteroscedastic regression; improved nonparametric estimation; model selection procedure; oracle inequality;
D O I：
10.17223/19988621/57/3
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The paper considers the problem of estimating the unknown function of heteroscedastic regression. An adaptive model selection procedure based on improved weighted estimates of least squares with specially selected weight coefficients is proposed. It is established that the procedure has a higher mean-square accuracy than the procedure based on classical weighted least-squares estimates. For the mean square risk of the proposed procedure, a non-asymptotic oracle inequality is proved that determines the exact upper bound for it in all possible estimates. The results of numerical simulation are given.
引用
收藏
页码：38 / 52
页数：15
相关论文
共 50 条
  • [31] An adaptive estimation for covariate-adjusted nonparametric regression model
    Li, Feng
    Lin, Lu
    Lu, Yiqiang
    Feng, Sanying
    [J]. STATISTICAL PAPERS, 2021, 62 (01) : 93 - 115
  • [32] Adaptive warped kernel estimation for nonparametric regression with circular responses
    Nguyen, Tien Dat
    Ngoc, Thanh Mai Pham
    Rivoirard, Vincent
    [J]. ELECTRONIC JOURNAL OF STATISTICS, 2023, 17 (02): : 4011 - 4048
  • [33] ESTIMATION IN LINEAR REGRESSION WITH HETEROSCEDASTIC VARIANCES
    RAO, JNK
    SUBRAHMA.K
    [J]. ANNALS OF MATHEMATICAL STATISTICS, 1970, 41 (02): : 756 - &
  • [34] Monte Carlo methods for nonparametric regression with heteroscedastic measurement error
    McIntyre, Julie
    Johnson, Brent A.
    Rappaport, Stephen M.
    [J]. BIOMETRICS, 2018, 74 (02) : 498 - 505
  • [35] Tests for the error distribution in nonparametric possibly heteroscedastic regression models
    Marie Hušková
    Simos G. Meintanis
    [J]. TEST, 2010, 19 : 92 - 112
  • [36] Tests for the error distribution in nonparametric possibly heteroscedastic regression models
    Huskova, Marie
    Meintanis, Simos G.
    [J]. TEST, 2010, 19 (01) : 92 - 112
  • [37] A nonparametric lack-of-fit test for heteroscedastic regression models
    Aubin, Jean-Baptiste
    Leoni-Aubin, Samuela
    [J]. COMPTES RENDUS MATHEMATIQUE, 2011, 349 (3-4) : 215 - 217
  • [38] Pointwise confidence intervals in nonparametric regression with heteroscedastic error structure
    Neumann, MH
    [J]. STATISTICS, 1997, 29 (01) : 1 - 36
  • [39] On a robust local estimator for the scale function in heteroscedastic nonparametric regression
    Boente, Graciela
    Ruiz, Marcelo
    Zamar, Ruben H.
    [J]. STATISTICS & PROBABILITY LETTERS, 2010, 80 (15-16) : 1185 - 1195
  • [40] A new nonparametric estimation method of the variance in a heteroscedastic model
    Zhang, Xiaoqin
    Hao, Hongxia
    Liang, Jiye
    [J]. HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2015, 44 (01): : 239 - 245
12345