Smooth simultaneous confidence bands for cumulative distribution functions

被引：24

作者：

Wang, Jiangyan ^{[1
]}

Cheng, Fuxia ^{[2
]}

Yang, Lijian ^{[1
,3
]}

机构：

[1] Soochow Univ, Sch Math Sci, Ctr Adv Stat & Econometr Res, Suzhou 215006, Peoples R China

[2] Illinois State Univ, Dept Math, Normal, IL 61790 USA

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

来源：

JOURNAL OF NONPARAMETRIC STATISTICS | 2013年 / 25卷 / 02期

基金：

美国国家科学基金会;

关键词：

bandwidth; confidence band; Holder continuity; kernel; Kolmogorov distribution; 62G08; 62G10; 62G20; NONPARAMETRIC-ESTIMATION; REGRESSION; ESTIMATOR;

D O I：

10.1080/10485252.2012.759219

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：

A plug-in kernel estimator is proposed for Holder continuous cumulative distribution function (cdf) based on a random sample. Uniform closeness between the proposed estimator and the empirical cdf estimator is established, while the proposed estimator is smooth instead of a step function. A smooth simultaneous confidence band is constructed based on the smooth distribution estimator and the Kolmogorov distribution. Extensive simulation study using two different automatic bandwidths confirms the theoretical findings.

引用

页码：395 / 407

页数：13

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