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2005-02

On the Optimality of Single-Group Designs in Linear Mixed Models

by Schmelter, T..


Series: 2005-02, Preprints

MSC:
62K05 Optimal designs
62J10 Analysis of variance and covariance
62H12 Estimation
62P10 Applications to biology and medical sciences

Abstract:
In this paper the class of designs for linear mixed models is considered where each individual is observed under a (possibly different) approximate design and the number of observations is the same for all individuals. It is then shown that the $\Phi$-optimal design in the class of balanced designs (single-group designs) for estimating the population parameters is also optimal in that wider class of designs mentioned before, where $\Phi$ is a convex and monotone criterion function that has to satisfy mild assumptions, which is e.g. the case for D-optimality and all linear criteria.

Keywords:
optimal design, mixed model, random coefficient regresion