An extension of a change-point problem

We consider a specific classification problem in the context of change-point detection. We present generalized classical maximum likelihood tests for homogeneity of the observed sample in a simple form which avoids the complex direct estimation of unknown parameters. This paper proposes a martingale...

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Published inStatistics (Berlin, DDR) Vol. 43; no. 3; pp. 213 - 225
Main Authors Vexler, Albert, Wu, Chengqing, Liu, Aiyi, Whitcomb, Brian W., Schisterman, Enrique F.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.06.2009
Subjects
change-point
classification
CUSUM statistics
Doob decomposition
likelihood ratio
limit of detection
martingale
martingale transforms
Primary: 62C25
Secondary: 60G46
Shiryayev-Roberts statistics
Online AccessGet full text
ISSN0233-1888
1029-4910
DOI10.1080/02331880802395930

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Abstract We consider a specific classification problem in the context of change-point detection. We present generalized classical maximum likelihood tests for homogeneity of the observed sample in a simple form which avoids the complex direct estimation of unknown parameters. This paper proposes a martingale approach to transformation of test statistics. For sequential and retrospective testing problems, we propose the adapted Shiryayev-Roberts statistics in order to obtain simple tests with asymptotic power one. An important application of the developed methods is in the analysis of exposure's measurements subject to limits of detection in occupational medicine.
AbstractList We consider a specific classification problem in the context of change-point detection. We present generalized classical maximum likelihood tests for homogeneity of the observed sample in a simple form which avoids the complex direct estimation of unknown parameters. This paper proposes a martingale approach to transformation of test statistics. For sequential and retrospective testing problems, we propose the adapted Shiryayev-Roberts statistics in order to obtain simple tests with asymptotic power one. An important application of the developed methods is in the analysis of exposure's measurements subject to limits of detection in occupational medicine.
Author Whitcomb, Brian W.
Liu, Aiyi
Vexler, Albert
Wu, Chengqing
Schisterman, Enrique F.
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SubjectTerms change-point
classification
CUSUM statistics
Doob decomposition
likelihood ratio
limit of detection
martingale
martingale transforms
Primary: 62C25
Secondary: 60G46
Shiryayev-Roberts statistics
Title An extension of a change-point problem
URI https://www.tandfonline.com/doi/abs/10.1080/02331880802395930
Volume 43
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