Recently replication methods have gained popularity for estimating variances in complex survey data analysis. One reason for this popularity is the relative simplicity of replication-based estimates, especially for nonlinear estimators; another is that modern computational capacity has made replication methods feasible for practical survey analysis. For details see Lohr (2009); Wolter (1985); Rust (1985); Dippo, Fay, and Morganstein (1984); Rao and Shao (1999); Rao, Wu, and Yue (1992); and Rao and Shao (1996).

Replication methods draw multiple replicates (also called subsamples) from a full sample according to a specific resampling scheme. The most commonly used resampling schemes are the balanced repeated replication (BRR) method and the jackknife method. For each replicate, the original weights are modified for the PSUs in the replicates to create replicate weights. The statistics of interest are estimated by using the replicate weights for each replicate. Then the variances of parameters of interest are estimated by the variability among the estimates derived from these replicates. You can use the REPWEIGHTS statement to provide your own replicate weights for variance estimation.