The Gaussian data assumption does not always lead to the largest CRB
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914457792282624 |
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| author | Delmas, Jean-Pierre Abeida, Habti |
| author_facet | Delmas, Jean-Pierre Abeida, Habti |
| contents | This lecture note addresses the common misconception that the Gaussian distribution always yields the largest Cramér-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06974 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Gaussian data assumption does not always lead to the largest CRB Delmas, Jean-Pierre Abeida, Habti Signal Processing Information Theory This lecture note addresses the common misconception that the Gaussian distribution always yields the largest Cramér-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. |
| title | The Gaussian data assumption does not always lead to the largest CRB |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2604.06974 |