Efficient replication variance estimation for two-phase sampling

Variance estimation for the regression estimator for a two-phase sample is investigated. A replication variance estimator with number of replicates equal to or slightly larger than the size of the second-phase sample is developed. In surveys where the second-phase sample is much smaller than the first-phase sample, the procedure has practical advantages. The method is similar in spirit to one of Fuller (1998), but is more easily applied and avoids some of that method's difficulties. The proposed method can be directly applied to variance estimation for the double expansion estimator and the reweighted expansion estimator. In these cases, the proposed method is asymptotically equivalent to the full jackknife, but uses a smaller number of replications.