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A new approach to optimal designs for correlated observations

Dette, H., Konstantinou, M. and Zhigljavsky, Anatoly 2017. A new approach to optimal designs for correlated observations. Annals of Statistics 45 (4) , pp. 1579-1608. 10.1214/16-AOS1500

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Abstract

This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of observations and considers the asymptotic properties of estimators and designs as the sample size converges to infinity, our approach is based on a continuous time model. We use results from stochastic anal- ysis to identify the best linear unbiased estimator (BLUE) in this model. Based on the BLUE, we construct an efficient linear estimator and corresponding optimal designs in the model for finite sample size by minimizing the mean squared error between the opti- mal solution in the continuous time model and its discrete approximation with respect to the weights (of the linear estimator) and the optimal design points, in particular in the multi-parameter case. In contrast to previous work on the subject the resulting estimators and corresponding optimal designs are very efficient and easy to implement. This means that they are practi- cally not distinguishable from the weighted least squares estimator and the corresponding optimal designs, which have to be found numerically by non-convex discrete optimization. The advantages of the new approach are illustrated in several numerical examples.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: linear regression, correlated observations, optimal design, Gaussian white mouse model, Doob representation, quadrature formulas
Additional Information: PDF uploaded in accordance with publisher's policies at http://www.sherpa.ac.uk/romeo/issn/0090-5364/(accessed 26.5.17).
Publisher: Institute of Mathematical Statistics
ISSN: 0090-5364
Date of First Compliant Deposit: 26 May 2017
Date of Acceptance: 13 March 2017
Last Modified: 31 Jan 2018 05:16
URI: http://orca.cf.ac.uk/id/eprint/100907

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