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Estimation of scale parameter under entropy loss function. (English) Zbl 0846.62021
Summary: Estimation of scale parameter under the entropy loss function is considered with restrictions to the principles of invariance and risk unbiasedness. An explicit form of minimum risk scale-equivariant estimator under entropy loss is obtained. The admissibility and inadmissibility of a class of linear estimators of the form \(cT + d\), where \(T \sim \Gamma (\nu, \eta)\), which includes the admissibility of the MRE estimator of the parameter of interest are studied.

MSC:
62F10 Point estimation
62C15 Admissibility in statistical decision theory
62F15 Bayesian inference
62A01 Foundations and philosophical topics in statistics
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