The Generalized Chernoff-Stein Lemma, Applications and Examples

TL;DR

This paper extends Stein's lemma to continuous and correlated scenarios by introducing $\

Contribution

It introduces $\\delta$-typicality and extends Stein's lemma to continuous and correlated data, broadening its applicability.

Findings

Extended Stein's lemma to continuous quantities.

Defined $\\delta$-typicality for entropy and relative entropy.

Applied results to Gaussian hypothesis testing with correlations.

Abstract

In this manuscript we define the notion of "$\delta$-typicality" for both entropy and relative entropy, as well as a notion of $\epsilon$-goodness and provide an extension to Stein's lemma for continuous quantities as well as correlated setups. We apply the derived results on the Gaussian hypothesis testing problem where the observations are possibly correlated.