Bhattacharyya Bounds without Regularity Assumptions

Abstract

In [1] a method for removing the regularity conditions from the Cramer-Rao Inequality was given and applied to the estimation of a single real parameter. It was noted there that the method would extend to problems more general than estimating a single real parameter. However, the method extends also for the estimation of a single real parameter and produces analogues of the Bhattacharyya bounds with and without nuisance parameters.