Asymptotic normality of kernel estimates in a regression model for random fields

被引：12

作者：

El Machkouri, Mohamed ^{[1
]}

Stoica, Radu ^{[2
]}

机构：

[1] Univ Rouen, Lab Math Raphael Salem, UMR CNRS 6085, F-76801 St Etienne, France

[2] Univ Lille 1, Lab Math Paul Painleve, UMR CNRS 8524, UFR Math Pures & Appl, F-59655 Villeneuve Dascq, France

来源：

JOURNAL OF NONPARAMETRIC STATISTICS | 2010年 / 22卷 / 08期

关键词：

nonparametric regression estimation; asymptotic normality; kernel estimator; strongly mixing random field; CENTRAL-LIMIT-THEOREM; DENSITY-ESTIMATION;

D O I：

10.1080/10485250903505893

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 establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On this basis, a statistical test that can be applied to image analysis is also presented.

引用

页码：955 / 971

页数：17

共 50 条

[41] The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data
Mohammedi, Mustapha
Bouzebda, Salim
Laksaci, Ali
JOURNAL OF MULTIVARIATE ANALYSIS, 2021, 181
[42] On asymptotic normality in nonlinear regression
Haupt, Harry
Oberhofer, Walter
STATISTICS & PROBABILITY LETTERS, 2009, 79 (06) : 848 - 849
[43] ASYMPTOTIC NORMALITY OF RANDOM-FIELDS OF POSITIVELY OR NEGATIVELY ASSOCIATED PROCESSES
ROUSSAS, GG
JOURNAL OF MULTIVARIATE ANALYSIS, 1994, 50 (01) : 152 - 173
[44] Local asymptotic mixed normality of transformed Gaussian models for random fields
Sei, Tomonari
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2007, 117 (03) : 375 - 398
[45] ASYMPTOTIC NORMALITY OF THE KERNEL QUANTILE ESTIMATOR
FALK, M
ANNALS OF STATISTICS, 1985, 13 (01): : 428 - 433
[46] Asymptotic normality of kernel functional regression estimator based upon twice censored data
Sarra, Leulmi
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2025, 54 (01) : 220 - 247
[47] Consistency and asymptotic normality of wavelet estimator in a nonparametric regression model
Shen, Aiting
Li, Xiang
Zhang, Yajing
Qiu, Yige
Wang, Xuejun
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2021, 93 (06) : 868 - 885
[48] Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model
Song, Yuping
Hou, Weijie
Yang, Guang
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2020, 22 (01) : 191 - 221
[49] Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model
Yuping Song
Weijie Hou
Guang Yang
Methodology and Computing in Applied Probability, 2020, 22 : 191 - 221
[50] ASYMPTOTIC NORMALITY OF M-ESTIMATES
ONISHCHENKO, VF
TSYBAKOV, AB
AUTOMATION AND REMOTE CONTROL, 1987, 48 (07) : 926 - 935

← 1 2 3 4 5 →