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Estimating the Shannon Entropy of Several Exponential Populations

Suchandan Kayal, Somesh Kumar

Abstract


The problem of estimating the Shannon’s entropy of several exponential populations using squared error as well as linex loss functions is considered when location parameters are known and scale parameters are unknown. Under the squared error loss function, the uniformly minimum variance unbiased estimator (UMVUE) is also a generalized Bayes estimator. We prove that it is admissible. A general inadmissibility result for the scale equivariant estimators is proved for both loss functions. Finally, under the linex loss function, a generalized Bayes estimator is shown to be admissible.

Keywords


uniformly minimum variance unbiased estimator, scale equivariant estimator, admissibility, generalized Bayes estimator, Brewster-Zidek technique

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