Optimal designs in regression with correlated errors

Dette, Holger, Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2016. Optimal designs in regression with correlated errors. Annals of Statistics 44 (1) , pp. 113-152. 10.1214/15-AOS1361

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Abstract

This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that asymptotically the new estimators achieve the same precision as the best linear unbiased estimator computed for the whole trajectory of the process. As a by-product, we derive explicit expressions for the BLUE in the continuous time model and analytic expressions for the optimal designs in a wide class of regression models. We also demonstrate that for a finite number of observations the precision of the proposed procedure, which includes the estimator and design, is very close to the best achievable. The results are illustrated on a few numerical examples.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Institute of Mathematical Statistics (IMS)
ISSN:	0090-5364
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	1 January 2016
Last Modified:	06 May 2023 03:42
URI:	https://orca.cardiff.ac.uk/id/eprint/84595

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