Remark on the finite-dimensional character of certain results of functional statistics

Jean-Marc Azaïs (1) , Jean-Claude Fort (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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.

Mots clés: functional statistics; small balls probability; finite dimension

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Marc Azaïs, Jean-Claude Fort. Remark on the finite-dimensional character of certain results of functional statistics. Comptes Rendus. Mathématique, 2013, 351 (3-4), p. 139-141. ⟨10.1016/j.crma.2013.02.004⟩. ⟨hal-00759922⟩