Decision‐Theoretic Estimation of the Product of Gamma Scales and Generalized Variance

Abstract

ABSTRACT:

The estimation of the product of scale parameters on the basis of n independent gamma distributed variables with known degrees of freedom is considered, Under squared error and entropy loss functions it is shown that the best equivariant estimator is admissible for n = 2, 3 and inadmissible for n ≥ 4. It follows that in the estimation problem cf generalized variance on the basis of a multivariate normal random sample with uriknown mean, the best multiple of the sample generalized variance is inadmissible if the dimension exceeds three and admissible within a well defined subclass of estimates if the dimension does not exceed three.