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On the optimality of group-wise balanced designs in a class of linear mixed models

by Schmelter, T..

Series: 2005-07, Preprints

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

We consider designs for linear mixed models where the vector of observations of one individual has the form $Y_i = F_i K_i \beta + F_i b_i + \epsilon_i$, with the matrices $K_i$ not depending on the chosen design. We show that for a broad class of criteria it is optimal for the estimation of the vector of population parameters $\beta$ to provide only one approximate design for each occuring shape of the $K_i$.

optimal design, mixed model, random coefficient regression, approximate design