606 – Sample Allocation
Empirical and Constrained Empirical Bayes Variance Estimation Under a One-Unit-Per-Stratum Sample Design
Sepideh Mosaferi
University of Maryland
A single primary sampling unit (PSU) per stratum design is a popular design for estimating the parameter of interest. Although, the point estimator of the design is unbiased and efficient, an unbiased variance estimator does not exist. A common method for the variance estimation of this design is based on collapsing or combining two adjacent strata, but the attained estimator of variance is not design-unbiased. If in some situations an unbiased estimator of variance is needed, the 1 PSU per stratum design with collapsed stratum variance estimator cannot be a good choice, and some statisticians prefer a design in which 2 PSUs per stratum are selected. In this talk, we first compare a 1 PSU per stratum design to a 2 PSUs per stratum design. Then, we propose an empirical Bayes estimator for the variance of 1 PSU per stratum design. To protect the over-shrinking in Empirical Bayes, we investigate the potential of the constrained empirical Bayes estimator. Using a simulation study, we show that the empirical Bayes and constrained empirical Bayes methods outperform the classical collapsed stratum variance method in terms of empirical relative man squared error.