On Complete Consistency for the Estimator of Nonparametric Regression Model Based on Asymptotically Almost Negatively Associated Errors

被引：3

作者：

Shen, Aiting ^{[1
]}

Zhang, Siyao ^{[2
]}

机构：

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

[2] Anhui Univ, Wendian Coll, Hefei 230601, Peoples R China

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2021年 / 23卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Complete consistency; Nonparametric regression model; Asymptotically almost negatively associated random variables; Bernstein type inequality; Nearest neighbor estimator; DEPENDENT RANDOM-VARIABLES; LARGE NUMBERS; COMPLETE CONVERGENCE; MULTIPLE-REGRESSION; STRONG LAW; ARRAYS; AANA;

D O I：

10.1007/s11009-020-09813-x

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, we mainly study the consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated (AANA, in short) errors. Firstly, the Bernstein type inequality for AANA random variables is established. By using the Bernstein type inequality and moment inequalities, we investigate the complete consistency and convergence rate for the estimator of nonparametric regression model based on AANA errors. As applications, the complete consistency and convergence rate for the nearest neighbor estimator are obtained.

引用

页码：1285 / 1307

页数：23

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