On least favourable two point priors and minimax estimators under absolute error loss

In case of absolute error loss the authors investigate for an arbitrary class of probability distributions, if or if not a two point prior can be least favourable and a corresponding Bayes estimator can be minimax when the parameter is restricted to a closed and bounded interval of ℝ. The general results are applied to several examples, for instance location and scale parameter families are considered. The authors give examples for which, independent of the length of the parameter interval, no two point priors exist. On the other hand examples are given having a least favourable two point prior when the parameter interval is sufficiently small.