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MODEL‐UNBIASEDNESS AND THE HORVITZ‐THOMPSON ESTIMATOR IN FINITE POPULATION SAMPLING
Author(s) -
Ho E. W. H.
Publication year - 1980
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1980.tb01170.x
Subject(s) - minimum variance unbiased estimator , mathematics , estimator , bias of an estimator , best linear unbiased prediction , statistics , efficient estimator , sampling design , stein's unbiased risk estimate , sample size determination , population , sampling (signal processing) , mean squared error , computer science , selection (genetic algorithm) , demography , filter (signal processing) , artificial intelligence , sociology , computer vision
Summary Under the, notion of superpopulation models, the concept of minimum expected variance is adopted as an optimality criterion for design‐unbiased estimators, i.e. unbiased under repeated sampling. In this article, it is shown that the Horvitz‐Thompson estimator is optimal among such estimators if and only if it is model‐unbiased, i.e. unbiased under the model. The family of linear models is considered and a sample design is suggested to preserve the model‐unbiasedness (and hence the optimality) of the Horvitz‐Thompson estimator. It is also shown that under these models the Horvitz‐Thompson estimator together with the suggested sample design is optimal among design‐unbiased estimators with any sample design (of fixed size n ) having non‐zero probabilities of inclusion for all population units.