Comparison of Variance Estimators for Self-Representing Primary Sample Units

Many surveys estimate variances with the balance repeated replication (BRR) variance estimator. With the self-representing (SR) Primary Sample Units (PSUs), surveys sometimes split them into parts which are then paired into pseudo strata and then BRR is applied to the pseudo strata. However, there is not much guidance on the number of pseudo strata to split the SR strata into or how (or if) the sort order should be used to split the sample when the sample was selected with systematic random sampling. Our research considered twelve different applications of the BRR variance estimators that varied by the number of pseudo strata formed and by how the sort order of a systematic random sample was used to split the PSU. We also included variations of the delete-a-group jackknife and successive difference replication variance estimators. Using simulations involving data from the Consumer Expenditures Survey, we found that the BRR variance estimator that split the sample of the SR PSUs into the most replicates possible and split the sample using the sort order was the best overall variance estimator for both national-level estimates and individual PSU-level estimates.