On a connection between Stein characterizations and Fisher information

TL;DR

This paper extends Stein characterizations of probability distributions by linking them to generalized Fisher information through a new factorization of the Stein operator, enhancing understanding of distributional properties.

Contribution

It introduces a generalized density approach to Stein characterizations and establishes a connection with information distances like Fisher information.

Findings

Stein operator factorization in terms of a generalized score function

Connection established between Stein characterizations and Fisher information

Enhanced understanding of distributional properties through generalized approaches

Abstract

We generalize the so-called density approach to Stein characterizations of probability distributions. We prove an elementary factorization property of the resulting Stein operator in terms of a generalized (standardized) score function. We use this result to connect Stein characterizations with information distances such as the generalized (standardized) Fisher information.