On UMV-estimators in survey sampling
When a sample has been drawn from a finite population in order to estimate the population total of a certain characteristic, there are many unbiased estimators to chose among and even restriction to- linear unbiased estimators does usually not single out a unique estimator. In such a case it seems natural to apply some optimality criterion, e.g. minimization of the variance. A famous theorem of Godambe states that the class of linear unbiased estimators does in general not contain an estimator with uniformly minimal variance; here `in general' means `provided the sampling design is not a unicluster design'. In the present paper various previously published proofs of this theorem are critically examined and a new proof is offered. Further some comments are given on the concept of necessary bestness, due to Prabhu-Ajgaonkar.
scientific article; zbMATH DE number 3436441