### 2005-07

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

Series: 2005-07, Preprints

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

Abstract:
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 $K_i$.

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