Bayes and equtvariant estimators of the variance of a finite population: part I, simple random sampling

The problem of estimating the variance of a finite population is studied in a Bayesian framework. On the basis of the moderntheoretical approach to sampling from finite populations and the special structure of the likelihood functions Bayes estimators of the population variance are derived. The structure of equivariant estimators is analyzed and Bayes equivariant estimators in the strict and the generalized sense are derived. The Bayes risk efficiency of the classical estimators is studied