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 19 条
[1]   NEW LOOK AT STATISTICAL-MODEL IDENTIFICATION [J].
AKAIKE, H .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1974, AC19 (06) :716-723
[2]   ANCOVA methods for heteroscedastic nonparametric regression models [J].
Akritas, MG ;
Van Keilegom, I .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2001, 96 (453) :220-232
[3]  
[Anonymous], 2006, Statistical Inference for Stochastic Processes, DOI [10.1007/s11203-005-3248-4, DOI 10.1007/S11203-005-3248-4]
[4]   Risk bounds for model selection via penalization [J].
Barron, A ;
Birgé, L ;
Massart, P .
PROBABILITY THEORY AND RELATED FIELDS, 1999, 113 (03) :301-413
[5]   ADAPTIVE VARIANCE FUNCTION ESTIMATION IN HETEROSCEDASTIC NONPARAMETRIC REGRESSION [J].
Cai, T. Tony ;
Wang, Lie .
ANNALS OF STATISTICS, 2008, 36 (05) :2025-2054
[6]  
Galtchouk L., 2004, MATH METHODS STAT, V13, P25
[7]   Adaptive sequential estimation for ergodic diffusion processes in quadratic metric [J].
Galtchouk, L. I. ;
Pergamenshchikov, S. M. .
JOURNAL OF NONPARAMETRIC STATISTICS, 2011, 23 (02) :255-285
[8]   Adaptive asymptotically efficient estimation in heteroscedastic nonparametric regression [J].
Galtchouk, Leonid ;
Pergamenshchikov, Sergey .
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2009, 38 (04) :305-322
[9]   Sharp non-asymptotic oracle inequalities for non-parametric heteroscedastic regression models [J].
Galtchouka, L. ;
Pergamenshchikovb, S. .
JOURNAL OF NONPARAMETRIC STATISTICS, 2009, 21 (01) :1-18
[10]  
Goldfeld S., 1972, NONLINEAR METHODS EC
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