Admissible and Minimax Estimators of a Lower Bounded Scale Parameter of a Gamma Distribution under the Entropy Loss Function
Abstract
This paper is concerned with admissible and minimax
estimation of scale parameter µ of a gamma distribution under
the entropy loss function, when it is known that µ > a for some
known a > 0. An admissible minimax estimator of µ, which is the
pointwise limit of a sequence of Bayes estimators, is derived. Also,
the admissible estimators and the only minimax estimator of µ in
the class of truncated linear estimators are obtained. Finally, the
results are extended to a subclass of scale parameter exponential
family and the family of transformed chi-square distributions.
estimation of scale parameter µ of a gamma distribution under
the entropy loss function, when it is known that µ > a for some
known a > 0. An admissible minimax estimator of µ, which is the
pointwise limit of a sequence of Bayes estimators, is derived. Also,
the admissible estimators and the only minimax estimator of µ in
the class of truncated linear estimators are obtained. Finally, the
results are extended to a subclass of scale parameter exponential
family and the family of transformed chi-square distributions.
Keywords
Admissibility; entropy loss function;
exponential family; gamma distribution; minimax estimation; trun-
cated parameter space.
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