Bayes Equivariant Estimators of the Variance of a Finite Population for Exponential Priors.

摘要

The paper presents the derivation of the Bayes equivariant estimator of the variance of a finite population for prior i.i.d. exponential random variables and quadratic loss. The forms of the Bayes equivariant estimator strongly depends on the prior distribution assumed. In a previous paper the form of the Bayes equivariant estimator was derived for normal i.i.d. random variables. This model yields a relatively simple result. The present paper is therefore devoted to the study of the form of the estimator when the prior distribution is considerably different from a normal distribution. Numerical illustrations are provided too. (Author)