Estimation Based on an Appropriate Choice of Loss Function

Some examples of absurd uniformly minimum variance unbiased estimators are discussed. Two reasons, argued in the literature, for having such estimators are lack of enough information in the available data and property of unbiasedness. In this paper, accepting both of these views, we show that an appropriate choice of loss function using a general concept of unbiasedness leads to risk unbiased, admissible and reasonable estimators. For this we extend the Rao- Blackwell theorem using a new way of defining unbiased estimator.