A new approach to optimal designs for correlated observations
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Date
2015
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Abstract
This paper presents a new and effcient 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.
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Keywords
linear regression, quadrature formulas, Doob representation, Gaussian white mouse model, optimal design, correlated observations