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 , 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 process is given that does not fulfill this assumption.
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Jean-Marc Azaïs 1 ; Jean-Claude Fort 2
@article{CRMATH_2013__351_3-4_139_0, author = {Jean-Marc Aza{\"\i}s and Jean-Claude Fort}, title = {Remark on the finite-dimensional character of certain results of functional statistics}, journal = {Comptes Rendus. Math\'ematique}, pages = {139--141}, publisher = {Elsevier}, volume = {351}, number = {3-4}, year = {2013}, doi = {10.1016/j.crma.2013.02.004}, language = {en}, }
TY - JOUR AU - Jean-Marc Azaïs AU - Jean-Claude Fort TI - Remark on the finite-dimensional character of certain results of functional statistics JO - Comptes Rendus. Mathématique PY - 2013 SP - 139 EP - 141 VL - 351 IS - 3-4 PB - Elsevier DO - 10.1016/j.crma.2013.02.004 LA - en ID - CRMATH_2013__351_3-4_139_0 ER -
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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