A Bayesian view of the Hammersley-Chapman-Robbins-type inequality

Abstract

From the Bayesian viewpoint, the information inequality applicable to the non-regular case is discussed. It is shown to construct an estimator which minimizes locally the variance of any estimator satisfying weaker conditions than the unbiasedness condition from which an information inequality is derived. The Hammersley-Chapman-Robbins inequality is also obtained as a special case of the inequality. An example is also given.