A variational interpretation of the Cramér–Rao bound

•Variational proofs of both the classic and the Bayesian Cramér-Rao bounds are presented.•The proofs allow for an alternative intrerpretation of the Cramér-Rao bound.•Based on this interpretation, a new family of CramérRao type bounds can be obtained. It is shown that both the classic and the Bayesi...

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Bibliographic Details
Published inSignal processing Vol. 182; p. 107917
Main Authors Fauß, Michael, Dytso, Alex, Poor, H. Vincent
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.05.2021
Subjects
Cramér–Rao bound
Fisher information
Variational techniques
62F10
65K10
Cramér–Rao bound
Variational techniques
62F15
Fisher information
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Summary:•Variational proofs of both the classic and the Bayesian Cramér-Rao bounds are presented.•The proofs allow for an alternative intrerpretation of the Cramér-Rao bound.•Based on this interpretation, a new family of CramérRao type bounds can be obtained. 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.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2020.107917