Gaussian Assumption: the Least Favorable but the Most Useful

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.