Modified balanced repeated replication for complex survey data

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Abstract
Balanced repeated replication, commonly used to estimate the variances of nonlinear estimators from stratified sampling designs, can run into problems in estimating a ratio of small domain totals or in the case of poststratification or unit nonresponse adjustment involving ratio weighting within cells if some cell sizes are small. This problem is mainly caused by a sharp perturbation of the weights to construct replicate estimates. To avoid extreme replicate estimates, Robert Fay proposed a modified balanced repeated replication method using gentler perturbation of weights. Theoretical properties of the modified method are studied here. The method is extended to the case of imputation for item nonresponse. Both smooth and nonsmooth estimators are studied.

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