Some Information Inequalities for Statistical Inference

TL;DR

This paper explores generalized information inequalities in statistical inference, extending classical bounds like Cramer-Rao and Bhattacharyya, and provides examples where these bounds are attained.

Contribution

It reinterprets Naudts's generalized Cramer-Rao bound and introduces new information inequalities that extend classical bounds to broader cases.

Findings

Examples where generalized bounds are attained

Extension of Bhattacharyya bounds to non-regular cases

Reinterpretation of Naudts's generalized Cramer-Rao bound

Abstract

In this paper, we first describe the generalized notion of Cramer-Rao lower bound obtained by Naudts (2004) using two families of probability density functions, the original model and an escort model. We reinterpret the results in Naudts (2004) from a statistical point of view and obtain some interesting examples in which this bound is attained. Further we obtain information inequalities which generalize the classical Bhattacharyya bounds in both regular and non-regular cases.