General weighted optimality of designed experiments

The standard approach to finding optimal experimental designs employs conventional measures of design efficacy, such as the $A$, $E$, and $D$-criterion, that assume equal interest in all estimable functions of model parameters. This paper develops a general theory for weighted optimality, allowing precise design selection according to expressed relative interest in different functions in the estimation space. The approach employs a very general class of matrix-specified weighting schemes that produce easily interpretable weighted optimality criteria. In particular, for any set of estimable functions, and any selected corresponding weights, analogs of standard optimality criteria are found that guide design selection according to the weighted variances of estimators of those particular functions. The results are applied to solve the $A$-optimal design problem for baseline factorial effects in unblocked experiments.