Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models

被引：41
|
作者：
Shen, Aiting [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2013年
基金：
中国国家自然科学基金;
关键词：
FIXED-DESIGN REGRESSION; MULTIPLE-REGRESSION; UNIFORM ASYMPTOTICS; RANDOM-VARIABLES; WEIGHTED SUMS; NOD SEQUENCE; STRONG LAW; THEOREMS;
D O I：
10.1155/2013/862602
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present the Bernstein-type inequality for widely dependent random variables. By using the Bernstein-type inequality and the truncated method, we further study the strong consistency of estimator of fixed design regression model under widely dependent random variables, which generalizes the corresponding one of independent random variables. As an application, the strong consistency for the nearest neighbor estimator is obtained.
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页数：9
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