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Title: A new approach to optimal designs for correlated observations
Authors: Dette, Holger 
Konstantinou, Maria 
Zhigljavsky, Anatoly 
Major Field of Science: Agricultural Sciences
Field Category: Environmental Biotechnology;Other Agricultural Sciences
Keywords: Correlated observations;Doob representation;Gaussian white mouse model;Linear regression;Optimal design;Quadrature formulas
Issue Date: 1-Aug-2017
Source: Annals of Statistics, 2017, vol. 45, no. 4, pp. 1579-1608
Volume: 45
Issue: 4
Start page: 1579
End page: 1608
Journal: Annals of Statistics 
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 analysis 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 optimal 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 multiparameter 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 practically not distinguishable from the weighted least squares estimator and the corresponding optimal designs, which have to be found numerically by nonconvex discrete optimization. The advantages of the new approach are illustrated in several numerical examples.
ISSN: 2168-8966
DOI: 10.1214/16-AOS1500
Rights: © Institute of Mathematical Statistics
Type: Article
Affiliation : Cardiff University 
Ruhr-Universität Bochum 
Cyprus University of Technology 
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