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A functional central limit theorem for regression models


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Bischoff, Wolfgang:
A functional central limit theorem for regression models.
In: Annals of statistics. 26 (1998) 4. - S. 1398-1410.
ISSN 0090-5364


Let a linear regression model be given with an experimental region $[a,b] \subseteq\R$ and regression functions $f_1,\dots, f_{d+1}: [a,b]\to \R$. 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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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
Titel an der KU entstanden:Nein
Eingestellt am:04. Mär 2010 12:43
Letzte Änderung:23. Dez 2014 09:20
URL zu dieser Anzeige:http://edoc.ku-eichstaett.de/3712/