A variational interpretation of the Cramér–Rao bound

Abstract

It is shown that both the classic and the Bayesian Cramér–Rao bounds can be obtained by minimizing the mean square error of an estimator while constraining the underlying distribution to be within a Fisher information ball. The presented results allow for some nonstandard interpretations of the Cramér–Rao bound and, more importantly, provide a template for novel bounds on the accuracy of estimators.