Probability Theory/Statistics
Remark on the finite-dimensional character of certain results of functional statistics
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
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
@article{CRMATH_2013__351_3-4_139_0,
     author = {Aza{\"\i}s, Jean-Marc and Fort, Jean-Claude},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.02.004/}
}
TY  - JOUR
AU  - Azaïs, Jean-Marc
AU  - Fort, Jean-Claude
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
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.02.004/
DO  - 10.1016/j.crma.2013.02.004
LA  - en
ID  - CRMATH_2013__351_3-4_139_0
ER  - 
%0 Journal Article
%A Azaïs, Jean-Marc
%A Fort, Jean-Claude
%T Remark on the finite-dimensional character of certain results of functional statistics
%J Comptes Rendus. Mathématique
%D 2013
%P 139-141
%V 351
%N 3-4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.02.004/
%R 10.1016/j.crma.2013.02.004
%G en
%F CRMATH_2013__351_3-4_139_0
Azaïs, Jean-Marc; Fort, Jean-Claude. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.02.004/

[1] Burba, Florent; Ferraty, Frédéric; Vieu, Philippe k-Nearest neighbour method in functional nonparametric regression, J. Nonparametr. Stat., Volume 21 (2009) no. 4, pp. 453-469

[2] Dabo-Niang, Sophie Estimation du mode dans un espace vectoriel semi-normé, C. R. Acad. Sci. Paris, Ser. I, Volume 339 (2004) no. 9, pp. 659-662 (in French)

[3] Ferraty, Frédéric; Goia, Aldo; Vieu, Philippe Régression non-paramétrique pour des variables aléatoires fonctionnelles mélangeantes, C. R. Acad. Sci. Paris, Ser. I, Volume 334 (2002) no. 3, pp. 217-220

[4] Ferraty, Frédéric; Kudraszow, Nadia; Vieu, Philippe Nonparametric estimation of a surrogate density function in infinite-dimensional spaces, J. Nonparametr. Stat., Volume 24 (2012) no. 2, pp. 447-464

[5] Ferraty, Frédéric; Laksaci, Ali; Tadj, Amel; Vieu, Philippe Rate of uniform consistency for nonparametric estimates with functional variables, J. Stat. Plan. Infer., Volume 140 (2010) no. 2, pp. 335-352

[6] Ferraty, F.; Van Keilegom, I.; Vieu, P. Regression when both response and predictor are functions, J. Multivariate Anal., Volume 109 (2012), pp. 10-28

[7] Li, Wenbo V.; Shao, Qi-Man Gaussian processes: Inequalities, small ball probabilities and applications (Rao, C.R.; Shanbhag, D., eds.), Stochastic Processes: Theory and Methods, Handbook of Statistics, vol. 19, Elsevier, New York, 2001, pp. 533-598

Cited by Sources: