Finding optimal estimators in survey sampling using unbiased estimators of zero

Minimum mean squared error linear unbiased estimation of the total of a finite population is investigated utilizing a characterization of such estimators involving unbiased estimators of zero. Assuming an equi-correlated regression superpopulation model, which covers many commonly used models as special cases, we use the new approach to derive necessary and sufficient conditions for existence of an optimal estimator, and the best estimator when it exists, under each of several criteria that emerge from taking either or both of the design and the model into account.