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Asymptotically optimal tests and optimal designs for testing the mean in regression models with applications to change-point problems

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Bischoff, Wolfgang ; Miller, Frank:
Asymptotically optimal tests and optimal designs for testing the mean in regression models with applications to change-point problems.
In: Annals of the Institute of Statistical Mathematics : AISM. 52 (2000) 4. - S. 658-679.
ISSN 0020-3157

Kurzfassung/Abstract

Let a linear regression model be given with an experimental region $[a,b] \subseteq\bbfR$ and regression functions $f_1,\dots, f_{d+1}: [a,b]\to \bbfR$. In practice it is an important question whether a certain regression function $f_{d+1}$, say, does or does not belong to the model. Therefore, we investigate the test problem $H_0$: ``$f_{d+1}$ does not belong to the model'' against $K$: ``$f_{d+1}$ belongs to the model'' based on the least-squares residuals of the observations made at design points of the experimental region $[a,b]$.\par By a new functional central limit theorem given by {\it W. Bischoff} [Ann. Stat. 26, No. 4, 1398-1410 (1998; Zbl 0936.62072)], we are able to determine optimal tests in an asymptotic way. Moreover, we introduce the problem of experimental design for the optimal test statistics. Further, we compare the asymptotically optimal test with the likelihood ratio test $(F$-test) under the assumption that the error is normally distributed. Finally, we consider real change-point problems as examples and investigate by simulations the behavior of the asymptotic test for finite sample sizes. We determine optimal designs for these examples.

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Publikationsform:Artikel
Schlagwörter:asymptotically optimal tests; F-test; Gaussian processes; quality control; likelihood ratio test; change-point problems
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Statistik und Stochastik
Peer-Review-Journal:Ja
Titel an der KU entstanden:Nein
Eingestellt am:04. Mär 2010 14:16
Letzte Änderung:04. Mär 2010 14:16
URL zu dieser Anzeige:http://edoc.ku-eichstaett.de/3706/