Comptes Rendus
Statistics
A Cramér–Rao inequality for non-differentiable models
Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 711-715.

We compute a variance lower bound for unbiased estimators in statistical models. The construction of the bound is related to the original Cramér–Rao bound, although it does not require the differentiability of the model. Moreover, we show our efficiency bound to be always greater than the Cramér–Rao bound in smooth models, thus providing a sharper result.

Nous obtenons une minoration pour la variance dʼun estimateur sans biais dans un modèle statistique. La construction de la borne est liée à celle de la borne de Cramér–Rao, mais elle ne nécessite pas dʼhypothèse de différentiabilité sur le modèle. De plus, nous montrons que la borne est toujours supérieure ou égale à la borne de Cramér–Rao dans les modèles différentiables, et fournit ainsi un résultat plus fort.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.08.005

Thibault Espinasse 1; Paul Rochet 1

1 Institut de mathématique de Toulouse, université Paul-Sabatier, 118, route de Narbonne, 31068 Toulouse cedex 9, France
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Thibault Espinasse; Paul Rochet. A Cramér–Rao inequality for non-differentiable models. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 711-715. doi : 10.1016/j.crma.2012.08.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.08.005/

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