Estimation in 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. In this paper we consider a subclass of the exponential families of distributions. Bayes estimator of a lower-bounded scale parameter, under the squared-log error loss function with a sequence of boundary supported priors is 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.
admissibility, Bayes estimator, truncated parameter spaces, squared-log error loss
62C10, 62C15, 62C20