An extension of the Csörgő-Horváth functional limit theorem and its applications to changepoint problems
type: Item
instance of: scholarly article
title: An extension of the Csörgő-Horváth functional limit theorem and its applications to changepoint problems
zbMATH Open document ID: 0812.60034
author: Dietmar Ferger
published in: Journal of Multivariate Analysis
publication date: 1994-12-11T00:00:00Z
review text: Let \(X^ n_ 1, \dots, X^ n_ n\), \(n \geq 1\), be a triangular array of rowwise independent random variables with values in a measurable space. Suppose there exists \(\theta \in[0,1)\) such that \(X^ n_ 1, \dots, X^ n_{[n \theta]}\) and \(X^ n_{[n \theta] + 1}, \dots, X^ n_ n\) have different unknown distributions. Let \(\Theta \subseteq (0,1]\). To test the hypothesis \(H_ 0 : \theta \in \Theta\) versus \(H_ 1 : \theta \notin \Theta\) the author proves a functional limit theorem for a suitable two-time parameter process \(\{b_ n : n \geq 1\}\). The proof is based on establishing tightness and convergence of the finite- dimensional distribution of \(\{b_ n : n \geq 1\}\) in the space \(D[0,1]^ 2\). Several applications to changepoint problems are given.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 701321
zbMATH Keywords: weak convergence
zbMATH Keywords: changepoint problems
zbMATH Keywords: functional limit theorem
zbMATH Keywords: two- time parameter process
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
full work available at URL: jmva.1994.1066
OpenAlex ID: W2067089149
DOI: 10.1006/JMVA.1994.1066
description: scientific article; zbMATH DE number 701321