The Annals of Statistics

Optimal designs in regression with correlated errors

Holger Dette, Andrey Pepelyshev, and Anatoly Zhigljavsky

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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.

Article information

Ann. Statist., Volume 44, Number 1 (2016), 113-152.

Received: January 2015
Revised: June 2015
First available in Project Euclid: 10 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs
Secondary: 31A10: Integral representations, integral operators, integral equations methods

Linear regression correlated observations signed measures optimal design BLUE Gaussian processes Doob representation


Dette, Holger; Pepelyshev, Andrey; Zhigljavsky, Anatoly. Optimal designs in regression with correlated errors. Ann. Statist. 44 (2016), no. 1, 113--152. doi:10.1214/15-AOS1361.

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