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An admissible minimax estimator of a lower-bounded scale parameter under squared-log error loss function. (English) Zbl 1227.62006
Summary: Estimation in a truncated parameter space is one of the most important features in statistical inference, because the frequently used criterion of unbiasedness is useless, since no unbiased estimator exists in general. So, other optimally criteria, such as admissibility and minimaxity, have to be looked for among others. We consider a subclass of exponential families of distributions. Bayes estimators of a lower-bounded scale parameter, under the squared-log error loss function with a sequence of boundary supported priors are obtained. An admissible estimator of a lower-bounded scale parameter, which is the limiting Bayes estimator, is given. Also another class of estimators of a lower-bounded scale parameter, which is called the truncated linear estimators, is considered and several interesting properties of the estimators in this class are studied. Some comparisons of the estimators in this class with an admissible estimator of a lower-bounded scale parameter are presented.

62C10 Bayesian problems; characterization of Bayes procedures
62C15 Admissibility in statistical decision theory
62F10 Point estimation
62C20 Minimax procedures in statistical decision theory
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