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Biometrika 1999 86(2):403-415; doi:10.1093/biomet/86.2.403
© 1999 by Biometrika Trust
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Modified balanced repeated replication for complex survey data

JNK RaoA1 and J ShaoA2

A1 School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5BS, Canada E-mail: jrao@math.carleton.ca A2 Department of Statistics, University of Wisconsin, Madison, WI 53706, USA E-mail: shao@stat.wisc.edu

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.

Key Words: Half-samples; Jackknife; Random grouping; Taylor linearisation; Variance estimation.


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