05-07
On the optimality of group-wise balanced designs in a class of linear mixed models
Preprint series: 05-07, Preprints
- MSC:
- 62K05 Optimal designs
- 62J10 Analysis of variance and covariance
- 62H12 Estimation
- 62P10 Applications to biology
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
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