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Residual Partial Sums Techniques for Fixed Designs to Find Change Points in Linear Regression

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Bischoff, Wolfgang:
Residual Partial Sums Techniques for Fixed Designs to Find Change Points in Linear Regression.
In: Computer modelling and new technologies. 14 (2010) 4. - S. 7-13.
ISSN 1407-5806 ; 1407-5814

Kurzfassung/Abstract

We investigate a data set describing the quality of a production process. By the information of these data it has to be decided whether the quality is constant or whether the quality changes. Our null hypothesis is that the quality is constant which is a linear regression. In practice it is popular to investigate the partial sums of the least squares residuals to look for changes in linear regression. The partial sums of the least squares residuals can be embedded into the class of continuous functions. By this procedure we obtain a stochastic process with continuous paths. It is called residual partial sum process. If the number of observations is large enough a projection of the Brownian motion can be considered as approximation (with respect to weak convergence) of the residual partial sum process. This projection of the Brownian motion can be used to establish nonparametric tests of Cramér-von Mises and Kolmogorov-Smirnov type to test for changes in linear regression. We use this procedure to test the data for constant quality.

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Publikationsform:Artikel
Schlagwörter:Residual partial sum limit processes, linear regression models, fixed designs, Brownian motion, projections of Brownian motion, reproducing kernel Hilbert space, change-point problem.
Sprache des Eintrags:Englisch
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Statistik und Stochastik
Peer-Review-Journal:Nein
Titel an der KU entstanden:Ja
KU.edoc-ID:6631
Eingestellt am: 10. Mär 2011 15:08
Letzte Änderung: 11. Jul 2013 15:33
URL zu dieser Anzeige: https://edoc.ku.de/id/eprint/6631/
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