Minimax optimality and the trinomial spike model

Minimaxdesign - konstruktion, effektivitetsjämförelser och praktiska tillämpninga

Optimal Allocation for Comparing Treatment Effects

Suppose the mean responses from m-1 treatment groups in an experiment are to be compared to the mean of a control group. A uniform allocation of observations over the treatment groups is then often used. However, other allocation schemes can give a better precision in the inference. This is particularly emphasised when the variances of the responses are different in different treatment groups. Here we consider optimal allocation according to the A- and D_{A}-criteria for the cases of equal as well as different variances of the responses in the treatment groups. We also consider the case when costs for observations are different in different treatment groups. As expected, optimal allocation depends on the variances of the responses in the treatment groups. If the variances are unknown, a minimax strategy can be used. This means that allocation is made subject to the worst case as the variances are varied within specified intervals. In general, minimax designs are difficult to find. However, for the case of treatment groups, as is considered here, we show that the minimax strategy is very simple to apply. The efficiency of allocations according to the minimax strategy is compared to the uniform as well as the locally optimal D_{A}- and A-optimal allocations