On a Theoretical Background for Computing Reliable Approximations of the Barankin Bound

Abstract

The Barankin bound is locally the greatest possible lower bound for the variance of any unbiased estimator of a deterministic pa- rameter, under certain relatively mild conditions. Much more essential, Barankin's work determines the su cient and necessary conditions un- der which an unbiased estimator with nite variance exists. Nevertheless, the computing of this bound, along with the proof of existence or non- existence of the estimator, has shown to be extremely challenging in most cases. Thereby, many approaches have been made to attain easily com- putable approximations of the bound, given it exists. Focusing on the rather central matter of existence, we provide a simple theoretical frame within which our approximations of the bound give a clear insight on whether an unbiased estimator does exist.