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

Details

Serval ID
serval:BIB_D5869188E620
Type
Article: article from journal or magazin.
Collection
Publications
Title
Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests
Journal
Metrika
Author(s)
Bischoff W., Hashorva E., Hüsler J., Miller F.
ISSN
0026-1335
1435-926X ([electronic])
Publication state
Published
Issued date
2005
Peer-reviewed
Oui
Volume
62
Number
1
Pages
85-98
Language
english
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. 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.
Keywords
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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Create date
03/09/2010 11:02
Last modification date
20/08/2019 15:55
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