Some Properties of Fay's Modified Balanced Repeated Replication

SUMMARY Balanced repeated replication (BRR) is commonly used to estimate the variances of nonlinear estimators from stratiied multistage sampling designs. The BRR method has wider application than the jackknife because of its ability to handle smooth estimators as well as nonsmooth estimators such as the sample median. However, the BRR can run into problems in estimating a ratio of small domain totals or in the case of poststratiication or unit nonresponse adjustment involving ratio weighting within cells if some cell sizes are small. This problem with BRR is mainly caused by a sharp perturbation of the weights to construct replicate estimates. Fay proposed a modiied BRR method using gentler perturbation of weights to avoid extreme replicate estimates. Theoretical properties of this method are studied here. The case of imputation for item nonresponse is also covered. Both smooth and nonsmooth estimators are studied.