A Procedure to Estimate the Population Mean in Random Effects Models

A general procedure for estimating the population mean in random effects models of the nested and/of classification type is considered. The suggested estimator is unbiased and consistent (with respect to the structure of the experimental design). It is also optimal with respect to a particular quadratic, location-sensitive criterion. Finally, for experimental designs which contain a certain degree of structural balance, the suggested estimator coincides with the sample mean.