Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests

Détails

ID Serval
serval:BIB_D5869188E620
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Titre
Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests
Périodique
Metrika
Auteur(s)
Bischoff W., Hashorva E., Hüsler J., Miller F.
ISSN
0026-1335
1435-926X ([electronic])
Statut éditorial
Publié
Date de publication
2005
Peer-reviewed
Oui
Volume
62
Numéro
1
Pages
85-98
Langue
anglais
Résumé
In practice, it is an important problem (especially in quality control) to secure that a known regression function occurs during a certain period in time. In the present paper, we consider the change-point problem that under the null hypothesis this known regression function occurs. As alternative, we consider a certain non-parametric class of functions that is of particular interest in quality control. We analyze this test problem by using partial sums of the data. Asymptotically, we get Brownian motion and Brownian motion with trend (not equal 0) under the hypothesis and under the alternative, respectively. We prove that tests based on partial sums have a larger power when the partial sums are taken from the time reversed data. This can be quantitatively determined in an asymptotic way by some new results on Kolmogorov type tests for Brownian motion with trend. We illustrate our results by a certain model that is interesting in quality control and by an example with real data.
Mots-clé
Change-point problem, Quality control, Regression models, Partial sums processes, Signal-plus-noise model, Brownian motion with trend, Tests of Kolmogorov type, Extreme values, Large deviations
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Création de la notice
03/09/2010 11:02
Dernière modification de la notice
20/08/2019 15:55
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