L1-CONSISTENCY OF THE KERNEL DENSITY ESTIMATORS BASED ON RANDOMLY RIGHT CENSORED-DATA

被引：4

作者：

GHORAI, JK ^{[1
]}

PATTANAIK, LM ^{[1
]}

机构：

[1] STILLMAN COLL, TUSCALOOSA, AL USA

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 1990年 / 19卷 / 08期

关键词：

Consistency; kernel density estimators; product limit estimator; randomly; right censored data;

D O I：

10.1080/03610929008830353

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：

Let fPL(x) be a kernel estimator of the density f(x) based on the product limit estimator of the distribution function F(x) associated with the density f(x). In this paper convergence properties of Jn(T) = ft-∞T | fPL(x)- f(x)|dx are established. In particular, it is shown that Jn(T) → 0 completely as n → ∞. Also it is shown that this complete convergence is equivalent to weak and strong convergence of Jn(T) to 0. © 1990, Taylor & Francis Group, LLC. All rights reserved.

引用

页码：2853 / 2870

页数：18

共 14 条

[1]

Blum JR., 1980, MAXIMAL DEVIATION TH, P213

[2] THE EQUIVALENCE OF WEAK, STRONG AND COMPLETE CONVERGENCE IN L1 FOR KERNEL DENSITY ESTIMATES [J].