A variational interpretation of the Cramer-Rao bound

It is shown that both the classic and the Bayesian Cramer-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 Cramer-Rao bound and, more importantly, provide a template for novel bounds on the accuracy of estimators. (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

Both the classic and Bayesian Cramer-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 results allow for nonstandard interpretations of the Cramer-Rao bound and provide a template for novel bounds on the accuracy of estimators.