Exact optimal designs for weighted least squares analysis with correlated errors

Dette, Holger, Kunert, Joachim and Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 2008. Exact optimal designs for weighted least squares analysis with correlated errors. Statistica Sinica 18 (1) , pp. 135-154.

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Abstract

In the common linear and quadratic regression model with an autoregressive error structure exact $D$-optimal designs for weighted least squares analysis are determined. It is demonstrated that for highly correlated observations the $D$-optimal design is close to the equally spaced design. Moreover, the equally spaced design is usually very efficient, even for moderate sizes of the correlation, while the $D$-optimal design obtained under the assumptions of independent observations yields a substantial loss in efficiency. We also consider the problem of designing experiments for weighted least squares estimation of the slope in a linear regression and compare the exact $D$-optimal designs for weighted and ordinary least squares analysis.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Autoregressive errors; linear regression; quadratic regression; exact D-optimal designs; estimation of the slope; generalized MANOVA
Publisher:	Academia Sinica, Institute of Statistical Science
ISSN:	1017-0405
Related URLs:	Publisher
Last Modified:	24 Oct 2022 11:42
URI:	https://orca.cardiff.ac.uk/id/eprint/49050

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