[Mode estimation in a semi-normed vectorial space.]
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.
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.
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Sophie Dabo-Niang 1, 2; Frédéric Ferraty 3, 4; Philippe Vieu 3
@article{CRMATH_2004__339_9_659_0, author = {Sophie Dabo-Niang and Fr\'ed\'eric Ferraty and Philippe Vieu}, 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}, }
TY - JOUR AU - Sophie Dabo-Niang AU - Frédéric Ferraty AU - Philippe Vieu 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 DO - 10.1016/j.crma.2004.09.006 LA - fr ID - CRMATH_2004__339_9_659_0 ER -
Sophie Dabo-Niang; Frédéric Ferraty; Philippe Vieu. Estimation du mode dans un espace vectoriel semi-normé. Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 659-662. doi : 10.1016/j.crma.2004.09.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.006/
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