Strassen's LIL for the Lorenz curve
type: Item
instance of: scholarly article
title: Strassen's LIL for the Lorenz curve
zbMATH Open document ID: 0868.60026
author: Ričardas Zitikis
author: Miklós Csörgo
published in: Journal of Multivariate Analysis
publication date: 1997-08-18T00:00:00Z
review text: The authors prove Strassen's law of the iterated logarithm for the Lorenz process assuming that the underlying d.f. \(F\) and its inverse \(F^{-1}\) are continuous and the moment \(EX^{2+u}\) is finite for some \(u>0\). Previously, the first author, \textit{S. Csörgö} and \textit{L. Horváth} [``An asymptotic theory for empirical reliability and concentration processes'' (1986; Zbl 0605.62105)] and \textit{R. C. Rao} and \textit{L. C. Zhao} [J. Multivariate Anal. 54, No. 2, 239-252 (1995)] proved strong invariance principle for Lorenz process using stronger assumptions on \(f\) and \(F\). Using a limit theorem for the general integrated empirical difference process and techniques of \textit{W. Vervaat} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 23, 245-253 (1972; Zbl 0238.60018)] and \textit{Polonik} (Shorack and Wellner, 1986), the authors are able to obtain sharper results for Lorenz process.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 954537
zbMATH Keywords: Lorenz curve
zbMATH Keywords: Strassen's law of the iterated logarithm
zbMATH Keywords: strong invariance principle
zbMATH Keywords: Lorenz process
reviewed by: Adhir K. Basu
MaRDI profile type: Publication
full work available at URL: jmva.1996.0050
OpenAlex ID: W1997473547
DOI: 10.1006/JMVA.1996.0050
description: scientific article; zbMATH DE number 954537