On weighted Fisher information matrix properties

TL;DR

This paper explores properties of weighted Fisher information matrices, extending known inequalities and identities, and offers new insights into entropy power concavity through generalized identities and bounds.

Contribution

It introduces an extended Fisher information inequality and a generalized De-Bruijn's identity, providing new theoretical insights into weighted Fisher information and entropy power.

Findings

Extended Fisher information inequality established.

New interpretation of entropy power concavity.

Bounds on weighted Fisher information discussed.

Abstract

In this paper, we review Fisher information matrices properties in weighted version and discuss inequalities/bounds on it by using reduced weight functions. In particular, an extended form of the Fisher information inequality previously established in [6] is given. Further, along with generalized De-Bruijn's identity, we provide new interpretation of the concavity for the entropy power.