Nous étudions un estimateur non paramétrique du mode de la densité d'une variable à valeurs dans un espace vectoriel semi-normé, de dimension éventuellement infinie. Nous établissons sa convergence presque sûre. Nous appliquons ce résultat au cas où la mesure de probabilité de la variable vérifie une condition de concentration.
We investigate a nonparametric estimate of the mode of a density function of a random variable taking values in a semi-normed vectorial space of eventually infinite dimension. The strong consistency of the estimate is shown. Special attention will be paid to apply our result to the case where the probability distribution of our random variable satisfies a concentration condition.
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@article{CRMATH_2004__339_9_659_0,
author = {Dabo-Niang, Sophie and Ferraty, Fr\'ed\'eric and Vieu, Philippe},
title = {Estimation du mode dans un espace vectoriel semi-norm\'e},
journal = {Comptes Rendus. Math\'ematique},
pages = {659--662},
publisher = {Elsevier},
volume = {339},
number = {9},
year = {2004},
doi = {10.1016/j.crma.2004.09.006},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.09.006/}
}
TY - JOUR AU - Dabo-Niang, Sophie AU - Ferraty, Frédéric AU - Vieu, Philippe TI - Estimation du mode dans un espace vectoriel semi-normé JO - Comptes Rendus. Mathématique PY - 2004 SP - 659 EP - 662 VL - 339 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.09.006/ DO - 10.1016/j.crma.2004.09.006 LA - fr ID - CRMATH_2004__339_9_659_0 ER -
%0 Journal Article %A Dabo-Niang, Sophie %A Ferraty, Frédéric %A Vieu, Philippe %T Estimation du mode dans un espace vectoriel semi-normé %J Comptes Rendus. Mathématique %D 2004 %P 659-662 %V 339 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.09.006/ %R 10.1016/j.crma.2004.09.006 %G fr %F CRMATH_2004__339_9_659_0
Dabo-Niang, Sophie; Ferraty, Frédéric; Vieu, Philippe. Estimation du mode dans un espace vectoriel semi-normé. Comptes Rendus. Mathématique, Tome 339 (2004) no. 9, pp. 659-662. doi : 10.1016/j.crma.2004.09.006. http://www.numdam.org/articles/10.1016/j.crma.2004.09.006/
[1] Simple estimation of the mode of a multivariate density, Canad. J. Statist., Volume 31 (2003), pp. 23-34
[2] Higher order analysis at Lebesgue points (Puri, M., ed.), Asymptotics in Statistics and Probability, VSP, 2001
[3] S. Dabo-Niang, F. Ferraty, P. Vieu, Mode estimation for functional random variable and its application for curves classification, Prépublication, 2003
[4] The functional nonparametric model and application to spectrometric data, Comput. Statist., Volume 17 (2002) no. 4, pp. 545-564
[5] Nonparametric estimation of the mode of a distribution of random curves, J. Roy. Statist. Soc. Ser. B, Volume 60 (1998) no. 4, pp. 681-691
[6] Gaussian processes: inequalities, small ball probabilities and applications, Stochastic Processes: Theory and Methods, Handbook of Statistics, vol. 19, North-Holland/Elsevier, Amsterdam, 2001
[7] On estimation of a probability density function and mode, Ann. Math. Statist., Volume 33 (1962), pp. 1065-1076
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