Estimating Renyi Entropy of Several Exponential Distributions Under an Asymmetric Loss Function

Abstract

The present paper takes into account the estimation of the Renyi entropy of several exponential distributions under a linex loss function. The models under study are (i) several exponential distributions with a common scale parameter and unknown but unequal location parameters and (ii) several exponential distributions with a common location parameter and unknown but unequal scale parameters. Improvements over the best affine equivariant estimator are obtained for the first model considering unrestricted and restricted parameter spaces. For the second model, sufficient conditions for improvement over affine and scale equivariant estimators are obtained and consequently, improvements over the maximum likelihood estimator and the uniformly minimum variance unbiased estimator are proposed. Sections on numerical studies have been included after each model to present comparative study of the relative risk performance of the proposed improved estimators.

Keywords

• Renyi entropy
• linex loss function
• equivariant estimator
• inadmissibility
• BrewsterZidek technique