Estimators, escort probabilities, and phi-exponential families in statistical physics

TL;DR

This paper generalizes the Cramer-Rao lower bound to pairs of probability distribution families, introducing phi-exponential families and exploring their dual structure, with implications for statistical physics.

Contribution

It introduces phi-exponential families and extends the Cramer-Rao bound to escort probability pairs, revealing their dual structure.

Findings

Generalized Cramer-Rao bound for escort families

Identification of optimal phi-exponential families

Analysis of dual structure in statistical physics

Abstract

The lower bound of Cramer and Rao is generalized to pairs of families of probability distributions, one of which is escort to the other. This bound is optimal for certain families, called phi-exponential in the paper. Their dual structure is explored.