A new approach to optimal design for linear models with correlated observations

Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279, Dette, Holger and Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 2010. A new approach to optimal design for linear models with correlated observations. Journal of the American Statistical Association 105 (491) , pp. 1093-1103. 10.1198/jasa.2010.tm09467

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Abstract

We consider the problem of designing experiments for regression in the presence of correlated observations with the location model as the main example. For a fixed correlation structure approximate optimal designs are determined explicitly, and it is demonstrated that under the model assumptions made by Bickel and Herzberg (1979) for the determination of asymptotic optimal design, the designs derived in this article converge weakly to the measures obtained by these authors. We also compare the asymptotic optimal design concepts of Sacks and Ylvisaker (1966, 1968) and Bickel and Herzberg (1979) and point out some inconsistencies of the latter. Finally, we combine the best features of both concepts to develop a new approach for the design of experiments for correlated observations, and it is demonstrated that the resulting design problems are related to the (logarithmic) potential theory.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Taylor & Francis
ISSN:	1537-274X
Last Modified:	15 May 2023 20:15
URI:	https://orca.cardiff.ac.uk/id/eprint/15206

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