A note on the universal consistency of the kernel distribution function estimator

被引：17

作者：

Chacon, Jose E. ^{[1
]}

Rodriguez-Casal, Alberto ^{[2
]}

机构：

[1] Univ Extremadura, Dept Matemat, Badajoz, Spain

[2] Univ Santiago de Compostela, Dept Estat & Invest Operat, Santiago De Compostela, Spain

来源：

STATISTICS & PROBABILITY LETTERS | 2010年 / 80卷 / 17-18期

关键词：

Data-dependent bandwidth; Distribution function; Kernel estimator; Minimal smoothness assumptions; Uniform in bandwidth consistency; DENSITY-FUNCTION; BANDWIDTH CONSISTENCY; UNIFORM; CONVERGENCE; INEQUALITY;

D O I：

10.1016/j.spl.2010.05.007

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：

The problem of universal consistency of data driven bandwidth selectors for the kernel distribution estimator is analyzed. We provide a uniform in bandwidth result for the kernel estimate of a continuous distribution function. Our smoothness assumption is minimal in the sense that if the true distribution function has some discontinuity then the kernel estimate is no longer consistent. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1414 / 1419

页数：6

共 23 条

[1]

[Anonymous], 1986, Probability and Measure

[2]

[Anonymous], 1964, Theory Probab Appl, DOI DOI 10.1137/1109069

[3] THE CONSISTENCY OF AUTOMATIC KERNEL DENSITY ESTIMATES [J].