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Biometrika 1990 77(2):365-375; doi:10.1093/biomet/77.2.365
© 1990 by Biometrika Trust
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On estimating distribution functions and quantiles from survey data using auxiliary information

J. N. K. RAO, J. G. KOVAR and H. J. MANTEL

Department of Mathematics & Statistics, Carleton University Ottawa, Canada K1S 5B6
Business Survey Methods Division Statistics Canada, Ottawa, Canada K1A 0T6
Department of Mathematics & Statistics, Carleton University Ottawa, Canada K1S 5B6

Ratio and difference estimators of a population distribution function under a general sampling design are obtained, using auxiliary population information. The relative mean errors and relative mean square errors of these estimators and a model-based estimator of Chambers & Dunstan (1986) are compared through a simulation study. The advantages of the design-based estimators over the model-based estimator under model misspecifications, especially for large samples, are demonstrated. Ratio and difference estimators of a population quantile are also studied.

Key Words: Conditional properties • Difference estimator • Model-based estimator • Model misspecification • Ratio estimator


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