Estimation of the Parameter in the Fisher Nile's Problem Under Entropy Loss

Abstract

Estimation of the parameter in the problem of the Nile is treated as a decision problem with entropy loss. It is shown that the minimum risk scale equivariant estimator dominates the incomplete sufficient unbiased estimators. Sharper bounds for the equivariant estimator are derived which may be used to obtain the values of the same from the sample with sufficient accuracy.