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

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Bischoff, Wolfgang ; Hashorva, Enkelejd ; Hüsler, Jürg ; Miller, Frank:
Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests.
In: Metrika. 62 (2005) 1. - S. 85-98.
ISSN 0026-1335 ; 1435-926x

Kurzfassung/Abstract

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. We consider the change-point problem that under the null hypothesis this known regression function occurs. As alternative, we consider a certain nonparametric 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 $(\not=$ 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.

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Publikationsform:Artikel
Schlagwörter: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
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Statistik und Stochastik
Peer-Review-Journal:Ja
Verlag:Springer
Die Zeitschrift ist nachgewiesen in:
Titel an der KU entstanden:Nein
KU.edoc-ID:2760
Eingestellt am: 23. Sep 2009 09:13
Letzte Änderung: 01. Jan 2010 21:33
URL zu dieser Anzeige: https://edoc.ku.de/id/eprint/2760/
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