Homogeneous Linear Estimator and Optimality in Finite Population Sampling
We recall Godambe’s theorem on the nonexistence of an umvue in finite population sampling for estimation of a population total and that the existence of a uniformly minimum mse estimator without any further conditions is not possible. Assuming model-unbiasedness with respect to a well known super population model, we give an alternative derivation of Royall’s optimum estimator. Finally, the role of design unbiasedness criterion is briefly discussed.
KeywordsHomogeneous linear estimator bias uniformly minimum mse estimator super population model
AMS Subject Classification62D05
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