The Gaussian data assumption does not always lead to the largest CRB

Jean-Pierre Delmas; Habti Abeida

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arXiv · 2604.06974

The Gaussian data assumption does not always lead to the largest CRB

Jean-Pierre Delmas·Habti Abeida

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Abstract

This lecture note addresses the common misconception that the Gaussian distribution always yields the largest Cram\'er-Rao Bound (CRB). We show that this property only holds under restrictive conditions: specifically, when the mean and covariance parameters are decoupled in the Fisher Information Matrix (FIM), when the parameter of interest lies in the mean vector and when there are no additive nuisance parameters. Beyond this framework, we provide counterexamples demonstrating that non-Gaussian distributions can produce larger CRB.

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Jean-Pierre Delmas, Habti Abeida. 2026-04-08. The Gaussian data assumption does not always lead to the largest CRB. https://arxiv.org/abs/2604.06974

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