The consistency for the estimator of nonparametric regression model based on martingale difference errors

被引：26

作者：

Chen, Zhiyong ^{[1
]}

Wang, Haibin ^{[1
]}

Wang, Xuejun ^{[2
,3
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[2] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China

[3] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

来源：

STATISTICAL PAPERS | 2016年 / 57卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Martingale difference sequence; Mean consistency; Complete consistency; Strong consistency; Nearest neighbor weights; DEPENDENT RANDOM-VARIABLES; COMPLETE CONVERGENCE; MULTIPLE-REGRESSION; SEQUENCES;

D O I：

10.1007/s00362-015-0662-6

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：

In this paper, by using the inequalities for martingale difference sequence, we investigate the consistency for the estimator of nonparametric regression model based on martingale difference errors. Some results on consistency for the estimator of are presented, including the mean consistency, complete consistency and strong consistency. As an application, the consistency for the nearest neighbor estimator is obtained.

引用

页码：451 / 469

页数：19

共 50 条

[21] Nonparametric regression with martingale increment errors
Delattre, Sylvain
Gaiffas, Stephane
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2011, 121 (12) : 2899 - 2924
[22] On the consistency of the P–C estimator in a nonparametric regression model
Yi Wu
Xuejun Wang
Narayanaswamy Balakrishnan
[J]. Statistical Papers, 2020, 61 : 899 - 915
[23] A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error's structure
Zhou, Xing-cai
Lin, Jin-guan
[J]. STATISTICS & PROBABILITY LETTERS, 2012, 82 (11) : 1914 - 1922
[24] WAVELET ESTIMATION IN NONPARAMETRIC MODEL UNDER MARTINGALE DIFFERENCE ERRORS
Liang Hanying 1 Zhang Dongxia 1 Lu Baoxian 2Dept.of Appl.Math.
[J]. Applied Mathematics:A Journal of Chinese Universities, 2004, (03) : 302 - 310
[25] COMPLETE CONSISTENCY AND ASYMPTOTIC NORMALITY FOR THE WEIGHTED ESTIMATOR IN A NONPARAMETRIC REGRESSION MODEL UNDER DEPENDENT ERRORS
Samura, Sallieu kabay
Wang, Shijie
Chen, Ling
Wang, Xuejun
Zhang, Fei
[J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2024, 18 (02): : 685 - 704
[26] Consistency of the Priestley-Chao estimator in nonparametric regression model with widely orthant dependent errors
He, Qihui
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2019, 2019 (1)
[27] Wavelet estimation in nonparametric model under martingale difference errors
Hanying L.
Dongxia Z.
Baoxian L.
[J]. Applied Mathematics-A Journal of Chinese Universities, 2004, 19 (3) : 302 - 310
[28] Consistency and asymptotic normality of wavelet estimator in a nonparametric regression model
Shen, Aiting
Li, Xiang
Zhang, Yajing
Qiu, Yige
Wang, Xuejun
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2021, 93 (06) : 868 - 885
[29] On the consistency of the P-C estimator in a nonparametric regression model
Wu, Yi
Wang, Xuejun
Balakrishnan, Narayanaswamy
[J]. STATISTICAL PAPERS, 2020, 61 (02) : 899 - 915
[30] On consistency of wavelet estimator in nonparametric regression models
Wang, Xuejun
Wu, Yi
Wang, Rui
Hu, Shuhe
[J]. STATISTICAL PAPERS, 2021, 62 (02) : 935 - 962

← 1 2 3 4 5 →