Empirical and Constrained Empirical Bayes Variance Estimation Under A One Unit Per Stratum Sample Design

TL;DR

This paper compares single and double PSU per stratum designs and introduces empirical Bayes variance estimators, including a constrained version, which outperform traditional methods in simulation studies.

Contribution

It proposes novel empirical Bayes and constrained empirical Bayes variance estimators for one PSU per stratum designs, improving accuracy over classical collapsed estimators.

Findings

Empirical Bayes estimators outperform classical methods in MSE.

Constrained empirical Bayes reduces bias in variance estimation.

Double PSU per stratum design offers better variance estimation than single PSU.

Abstract

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 practice to solve this is to collapse or combine the two adjacent strata, but the attained estimator of variance is not design-unbiased, and the bias increases as the population means of the collapsed strata become more variant. Therefore, the one PSU per stratum design with collapsed stratum variance estimator might not be a good choice, and some statisticians prefer a design in which two PSUs per stratum are selected. In this paper, we first compare a one PSU per stratum design to a two PSUs per stratum design. Then, we propose an empirical Bayes estimator for the variance of one PSU per stratum design, where it over-shrinks towards the prior mean. To protect against this, we investigate the potential of a constrained empirical Bayes estimator. Through a simulation study, we show that the empirical Bayes and constrained empirical Bayes estimators outperform the classical collapsed one in terms of empirical relative mean squared error.