Extended Glivenko-Cantelli Theorem in Nonparametric Regression

被引：2

作者：

Cheng, Fuxia ^{[1
]}

Yan, Jigao ^{[2
]}

Yang, Lijian ^{[3
,4
]}

机构：

[1] Illinois State Univ, Dept Math, Normal, IL 61761 USA

[2] Soochow Univ, Sch Math Sci, Suzhou 215006, Peoples R China

[3] Ctr Adv Stat & Econometr Res, Suzhou, Peoples R China

[4] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2014年 / 43卷 / 17期

关键词：

Empirical process; Glivenko-Cantelli theorem; Nonparametric regression; Residuals; DISTRIBUTION FUNCTION ESTIMATORS; STRONG UNIFORM CONSISTENCY; ERROR DENSITY;

D O I：

10.1080/03610926.2012.700377

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 consider the uniform strong consistency of the cumulative distribution function estimator in nonparametric regression. We obtain the extended Glivenko-Cantelli theorem for the residual-based empirical distribution function.

引用

页码：3720 / 3725

页数：6

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