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On exact D-optimal designs for regression models with correlated observations

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Bischoff, Wolfgang:
On exact D-optimal designs for regression models with correlated observations.
In: Annals of the Institute of Statistical Mathematics : AISM. 44 (1992). - S. 229-238.
ISSN 0020-3157

Kurzfassung/Abstract

Let $\tau\sp*$ be an exact $D$-optimal design for a given regression model $Y\sb \tau=X\sb \tau \beta+Z\sb \tau$. Sufficient conditions are given for designing how the covariance matrix of $Z\sb \tau$ may be changed so that not only $\tau\sp*$ remains $D$-optimal but also that the best linear unbiased estimator (BLUE) of $\beta$ stays fixed for the design $\tau\sp*$, although the covariance matrix of $Z\sb{\tau\sp*}$ is changed. Hence under these conditions a best, according to $D$- optimality, BLUE of $\beta$ is known for the model with the changed covariance matrix.\par The results may also be considered as determination of exact $D$-optimal designs for regression models with special correlated observations where the covariance matrices are not fully known. Various examples are given, especially for regression with intercept term, polynomial regression, and straight-line regression. A real example in electrocardiography is treated shortly.

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Publikationsform:Artikel
Schlagwörter:correlated observations; robustness against disturbances; exact $D$- optimal design; best linear unbiased estimator; changed covariance matrix; intercept term; polynomial regression; straight-line regression; electrocardiography
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:19. Mär 2010 15:36
Letzte Änderung:19. Mär 2010 15:36
URL zu dieser Anzeige:http://edoc.ku-eichstaett.de/3819/