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
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