Gaussian Assumption: the Least Favorable but the Most Useful

TL;DR

This paper demonstrates that assuming Gaussian noise simplifies analysis and provides worst-case bounds, making it a valuable approximation despite its conservative nature.

Contribution

It connects existing results with information theory, justifies the Gaussian assumption's worst-case property, and extends this to correlated observations.

Findings

Gaussian assumption yields the largest CRLB.

Connection between classical results and information theory.

Extension to correlated observations.

Abstract

This paper focuses on three contributions. First, a connection between the result, proposed by Stoica and Babu, and the recent information theoretic results, the worst additive noise lemma and the isoperimetric inequality for entropies, is illustrated. Second, information theoretic and estimation theoretic justifications for the fact that the Gaussian assumption leads to the largest Cram\'{e}r-Rao lower bound (CRLB) is presented. Third, a slight extension of this result to the more general framework of correlated observations is shown.