Attainments of the Bayesian information bounds for the escort distribution (Bayesian approaches and statistical inference)

Abstract

We show some necessary and sufficient conditions for the attainment of the Borovkov-Sakhanenko and van Trees Bayesian information bounds when the underlying distribution is the escort distribution of an exponential family and the conjugate or the Jeffreys prior. In this paper we consider the case where the order of the escort distribution is a constant and the parameter of exponential family is a random variable. Some examples attaining the bounds are also given