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Minimum Variance Estimation in Stratified Sampling

James Bethel
Journal of the American Statistical Association
Vol. 84, No. 405 (Mar., 1989), pp. 260-265
DOI: 10.2307/2289872
Stable URL: http://www.jstor.org/stable/2289872
Page Count: 6
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Minimum Variance Estimation in Stratified Sampling
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Abstract

This article discusses efficiency properties of some common stratified estimators, in the context of a superpopulation model, relative to the greatest lower bound on the variance of the Horvitz-Thompson estimator. The estimators discussed use both Dalenius-Hodges and model-based survey sampling (MBSS) stratification and a variety of sample allocation methods, including optimum, proportionate, and uniform sample allocation. The main result is that both Dalenius-Hodges stratification with optimal allocation and MBSS stratification with uniform allocation yield approximately minimum variance estimators, with convergence to the lower bound at rate O(L-2), where L is the number of strata. Since this lower bound has been shown to hold for many types of finite population estimators, the results derived here have broad implications. A series of examples is presented in which Dalenius-Hodges/optimum allocation is consistently more efficient than MBSS/uniform allocation.

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