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
收藏
页码：451 / 469
页数：19
相关论文
共 50 条
  • [31] On consistency of wavelet estimator in nonparametric regression models
    Xuejun Wang
    Yi Wu
    Rui Wang
    Shuhe Hu
    [J]. Statistical Papers, 2021, 62 : 935 - 962
  • [32] Consistency for the least squares estimator in nonparametric regression
    VandeGeer, S
    Wegkamp, M
    [J]. ANNALS OF STATISTICS, 1996, 24 (06): : 2513 - 2523
  • [33] Complete consistency of the estimator of nonparametric regression model under ND sequence
    Wang, Xuejun
    Si, Zeyu
    [J]. STATISTICAL PAPERS, 2015, 56 (03) : 585 - 596
  • [34] Complete consistency of the estimator of nonparametric regression model under ND sequence
    Xuejun Wang
    Zeyu Si
    [J]. Statistical Papers, 2015, 56 : 585 - 596
  • [35] On complete consistency for the weighted estimator of nonparametric regression models
    Rui Zhang
    Yi Wu
    Weifeng Xu
    Xuejun Wang
    [J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019, 113 : 2319 - 2333
  • [36] On complete consistency for the weighted estimator of nonparametric regression models
    Zhang, Rui
    Wu, Yi
    Xu, Weifeng
    Wang, Xuejun
    [J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2019, 113 (03) : 2319 - 2333
  • [37] The consistency of estimator under fixed design regression model with NQD errors
    Jianhua Shi
    Xiaoping Chen
    Yong Zhou
    [J]. Journal of Inequalities and Applications, 2014
  • [38] Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples
    Liwang Ding
    Ping Chen
    Yongming Li
    [J]. Statistical Papers, 2020, 61 : 2331 - 2349
  • [39] The consistency of estimator under fixed design regression model with NQD errors
    Shi, Jianhua
    Chen, Xiaoping
    Zhou, Yong
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
  • [40] Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples
    Ding, Liwang
    Chen, Ping
    Li, Yongming
    [J]. STATISTICAL PAPERS, 2020, 61 (06) : 2331 - 2349
12345