A variational interpretation of the Cramér–Rao bound

Michael Fauß, Alex Dytso, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageEnglish (US)
Article number107917
JournalSignal Processing
StatePublished - May 2021

All Science Journal Classification (ASJC) codes

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


  • Cramér–Rao bound
  • Fisher information
  • Variational techniques


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