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February 2016 Optimal designs in regression with correlated errors
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
Ann. Statist. 44(1): 113-152 (February 2016). DOI: 10.1214/15-AOS1361

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.

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Holger Dette. Andrey Pepelyshev. Anatoly Zhigljavsky. "Optimal designs in regression with correlated errors." Ann. Statist. 44 (1) 113 - 152, February 2016. https://doi.org/10.1214/15-AOS1361

Information

Received: 1 January 2015; Revised: 1 June 2015; Published: February 2016
First available in Project Euclid: 10 December 2015

zbMATH: 1338.62161
MathSciNet: MR3449764
Digital Object Identifier: 10.1214/15-AOS1361

Subjects:
Primary: 62K05
Secondary: 31A10

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

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 1 • February 2016
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