Joint approximation of processes based on spacings and order statistics
type: Item
instance of: scholarly article
title: Joint approximation of processes based on spacings and order statistics
zbMATH Open document ID: 0813.62045
DOI: 10.1016/0304-4149(94)90069-8
published in: Stochastic Processes and their Applications
publication date: 1995-06-06T00:00:00Z
review text: The author considered the joint behaviour of two empirical processes created by a sequence of i.i.d. r.v. \(\omega_ 1, \omega_ 2, \dots\). The first one is \(n^{-1} \sum_{i=1}^ n I_{S_ i/ S_{n+1}\leq x}\), and the second corresponds to the spacings empirical distribution function \(n^{-1} \sum^ n_{i=1} I_{F( n\omega_ i/ S_{n+1})\leq x}\), where \(S_ i= \omega_ 1+ \dots+ \omega_ i\). Under some conditions on the distribution of the \(\omega_ i\) the joint approximation is given. The proof is based on the approximation of the uniform empirical process by a Kiefer process and consists of two steps - - approximation of the process related to the renewal empirical distribution function and the one related to the inverse of it.
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 713909
zbMATH Keywords: empirical processes
zbMATH Keywords: spacings empirical distribution
zbMATH Keywords: joint approximation
zbMATH Keywords: Kiefer process
zbMATH Keywords: renewal empirical distribution
author: Philippe Barbe
reviewed by: Stefanka Chukova
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90069-8
OpenAlex ID: W2053656607
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description: scientific article; zbMATH DE number 713909