Characterization of weak convergence for smoothed empirical and quantile processes under phi-mixing

被引：2

作者：

Degenhardt, HJA

Puri, ML

Sun, S

vanZuijlen, MCA

机构：

[1] CATHOLIC UNIV NIJMEGEN,DEPT MATH,NL-6525 ED NIJMEGEN,NETHERLANDS

[2] INDIANA UNIV,BLOOMINGTON,IN 47405

[3] TEXAS TECH UNIV,LUBBOCK,TX 78409

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1996年 / 53卷 / 03期

关键词：

smoothed empirical processes; smoothed sample quantiles; weak convergence; phi-mixing;

D O I：

10.1016/0378-3758(95)00133-6

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 {X(n), n greater than or equal to 1} be a sequence of phi-mixing random variables having a smooth common distribution function F. The smoothed empirical distribution function is obtained by integrating a kernel type density estimator. In this paper we provide necessary and sufficient conditions for the central limit theorem to hold for smoothed empirical distribution functions and smoothed sample quantiles. Also, necessary and sufficient conditions are given for weak convergence of the smoothed empirical process and the smoothed uniform quantile process.

引用

页码：285 / 295

页数：11

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