Homogeneous Linear Estimator and Optimality in Finite Population Sampling

Abstract

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.

Keywords:

• 62D05

Keywords:

• Homogeneous linear estimator
• bias
• uniformly minimum mse estimator
• super population model

Acknowledgment

The author thanks Prof. Bikas Sinha for his helpful comments and discussions and an associate editor and referees for their useful suggestions and remarks.