Comptes Rendus
no. 3-4
Probability Theory/Statistics
Remark on the finite-dimensional character of certain results of functional statistics

Presented by: Jean-Pierre Kahane

Jean-Marc Azaïs1; Jean-Claude Fort2
1 Université de Toulouse, IMT, ESP, 31062 Toulouse cedex 9, France
2 Université Paris-Descartes, SPC, MAP5, 45, rue des Saints-Pères, 75006 Paris, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 139-141.

This note shows that some assumption on small balls probability, frequently used in the domain of functional statistics, implies that the considered functional space is of finite dimension. To complete this result an example of L2 process is given that does not fulfill this assumption.

Cette note montre quʼune hypothèse concernant les probabilités de petites boules, fréquemment utilisée en statistique fonctionnelle, implique que la dimension de lʼespace fonctionnel considéré est finie. Un exemple de processus L2, ne vérifiant pas cette hypothèse, vient compléter ce résultat.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.02.004

Jean-Marc Azaïs 1; Jean-Claude Fort 2

1 Université de Toulouse, IMT, ESP, 31062 Toulouse cedex 9, France
2 Université Paris-Descartes, SPC, MAP5, 45, rue des Saints-Pères, 75006 Paris, France 
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Jean-Marc Azaïs; Jean-Claude Fort. Remark on the finite-dimensional character of certain results of functional statistics. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 139-141. doi : 10.1016/j.crma.2013.02.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.004/

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