no. 3-4
Probability Theory/Statistics
Remark on the finite-dimensional character of certain results of functional statistics
[Remarque sur le caractère fini-dimensionnel de certains résultats de statistique fonctionnelle]

Présenté par : Jean-Pierre Kahane

Azaïs, Jean-Marc1 ; Fort, Jean-Claude2
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, Tome 351 (2013) no. 3-4, pp. 139-141.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.02.004
Azaïs, Jean-Marc 1 ; Fort, Jean-Claude 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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Azaïs, Jean-Marc; Fort, Jean-Claude. Remark on the finite-dimensional character of certain results of functional statistics. Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 139-141. doi : 10.1016/j.crma.2013.02.004. http://www.numdam.org/articles/10.1016/j.crma.2013.02.004/

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