  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.
