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Exact optimal designs for weighted least squares analysis with correlated errors

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

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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: 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
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Last Modified: 24 Oct 2022 11:42

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