Abstract
ABSTRACT As a typical non-regular case, we consider a family of symmetrically truncated normal distributions with a location parameter θ. The information inequalities for the Bayes risk of any estimator of θ are asymptotically given up to the higher order. The asymptotic lower bounds for the Bayes risk are shown to be sharp up to the higher order. The comparison of the Bayes risks of the mid-range, the maximum likelihood estimator and the maximum probability estimator is done, and, from the viewpoint of the asymptotic concentration probability, that of the estimators is also provided.
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