Detecting change in a random sequence
type: Item
instance of: scholarly article
title: Detecting change in a random sequence
zbMATH Open document ID: 0641.62049
DOI: 10.1016/0047-259X(87)90181-3
author: Lajos Horváth
author: Miklós Csörgo
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: This paper proposes a sequential procedure for detecting a change-point in a sequence of i.i.d. random observations \(X_ 1,X_ 2,..\). in a nonparametric framework. The sequential test statistic is based upon the empirical distribution function of variables \(E_ i\) which act as the recursive residuals in the Gaussian linear model: \(E_ i\) is the e.d.f. of the i-1 previous observations, taken at the value \(X_ i.\) Under the null hypothesis, the variables \(E_ i\) are quite uniformly distributed and the authors give the asymptotic threshold for various weighted statistics and a fixed level, using the approximation by a Kiefer process. They then prove the consistency of the proposed test.
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4044975
zbMATH Keywords: change point problem
zbMATH Keywords: strong approximations
zbMATH Keywords: sequential ranks
zbMATH Keywords: boundary crossing problems
zbMATH Keywords: sequential test statistic
zbMATH Keywords: empirical distribution
zbMATH Keywords: recursive residuals
zbMATH Keywords: Gaussian linear model
zbMATH Keywords: asymptotic threshold
zbMATH Keywords: weighted statistics
zbMATH Keywords: approximation by a Kiefer process
zbMATH Keywords: consistency
MaRDI profile type: Publication
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full work available at URL: 0047-259x(87)90181-3
OpenAlex ID: W1558022921
description: scientific article; zbMATH DE number 4044975