Finding Optimal Estimators in Survey Sampling Using Un- Biased Estimators of Zero

Minimum mean squared error linear unbiased estimation of the total of a nite population is investigated utilizing a characterization of such estimators involving unbiased estimators of zero. Several criteria emerging from taking either or both of the design and a model into account are discussed. For each criterion, necessary and su cient conditions for existence of a best estimator and the optimal estimator, when it exists, are derived using our uni ed approach. The results are presented for an equi-correlated regression superpopulation model, which includes many commonly used models as special cases.