On the Vervaat and Vervaat-error processes

被引：6

作者：

Csörgo, M

Zitikis, R

机构：

[1] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

[2] Univ Manitoba, Dept Stat, Winnipeg, MB R3T 2N2, Canada

[3] Carleton Univ, Lab Res Stat & Probabil, Ottawa, ON K1S 5B6, Canada

来源：

ACTA APPLICANDAE MATHEMATICAE | 1999年 / 58卷 / 1-3期

关键词：

Vervaat process; Vervaat-error process; empirical process; quantile process; Bahadur-Kiefer process; Kiefer process; Brownian bridge; Wiener process; strong approximations; laws of the iterated logarithm; convergence in distribution;

D O I：

10.1023/A:1006329502117

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It has been known since the pioneering works of Wim Vervaat in the early 70's that the appropriately normalized Vervaat process asymptotically behaves like one half times the squared empirical process. In this paper we present a survey of the results concerning various distances between the Vervaat process and one half times the squared empirical process. In particular, the pointwise, L-p-, and sup-distances between these two processes are given full consideration.

引用

页码：91 / 105

页数：15

共 31 条

[1] ASYMPTOTIC THEORY OF CERTAIN GOODNESS OF FIT CRITERIA BASED ON STOCHASTIC PROCESSES [J].