A variational interpretation of the Cramér–Rao bound

Michael Fauß; Alex Dytso; H. Vincent Poor

doi:10.1016/j.sigpro.2020.107917

A variational interpretation of the Cramér–Rao bound

Michael Fauß, Alex Dytso, H. Vincent Poor

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English (US)
Article number	107917
Journal	Signal Processing
Volume	182
DOIs	https://doi.org/10.1016/j.sigpro.2020.107917
State	Published - May 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Software
Signal Processing
Computer Vision and Pattern Recognition
Electrical and Electronic Engineering

Keywords

Cramér–Rao bound
Fisher information
Variational techniques

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10.1016/j.sigpro.2020.107917

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abstract = "It is shown that both the classic and the Bayesian Cram{\'e}r–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 Cram{\'e}r–Rao bound and, more importantly, provide a template for novel bounds on the accuracy of estimators.",

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AB - 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.

KW - Cramér–Rao bound

KW - Fisher information

KW - Variational techniques

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ER -

A variational interpretation of the Cramér–Rao bound

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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