repeated replication (BRR) is a method to estimate the sampling variability
of a statistic that takes into account the properties of the sample
design. It provides unbiased estimates of the sampling error arising from
selection procedures. The estimates capture the effects of stratification,
clustering, and unequal probabilities of selection.
BRR works by repeatedly re-estimating the target statistics using half the sample at a time. When each sampling stratum contains two PSUs, replicates are formed by including one of the two PSUs from a stratum. If the sample includes H strata, such replicates can be formed.The variability of the target statistics across these replicates offers an estimate of the sampling variance of the estimates.
Fay’s method is a variant of Balanced Repeated Replication in which less extreme adjustments are made to the weights for each replicate.For example, the “included” PSUs may have their weights increased by 50%, and the excluded PSUs would have their weights decreased by a corresponding amount.