A geometer's view of the the Cram\'er-Rao bound on estimator variance

TL;DR

This paper revisits the Cramér-Rao bound, a fundamental limit on estimator variance, by reformulating its statement and proof through modern geometric perspectives, enhancing conceptual understanding.

Contribution

It introduces a geometric reinterpretation of the classical Cramér-Rao bound, providing new insights into its foundational structure.

Findings

Reformulation of the Cramér-Rao bound using geometric language

Enhanced conceptual understanding of estimator variance limits

Potential for applying geometric methods to statistical bounds

Abstract

The classical Cram\'er-Rao inequality gives a lower bound for the variance of a unbiased estimator of an unknown parameter, in some statistical model of a random process. In this note we rewrite the statment and proof of the bound using contemporary geometric language.