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Comptes Rendus Mathématique
Volume 334, n° 7
pages 597-602 (2002)
Doi : S1631-073X(02)02311-7
Received : 20 Mars 2001 ; 
Sur quelques résultats de convergence dans l'inférence d'une classe de processus ponctuels
Convergence results for point processes estimators
 

Aboubakary Diakhaby a, b
a UFR de mathématiques appliquées et d'informatique, Université Gaston Berger, BP 234, Saint-Louis, Sénégal 
b Équipe PRISME, Université René Descartes, UFR de mathématiques et informatique, 45, rue des Saints-Pères, 75270 Paris cedex 06, France 

Note présentée par Paul Deheuvels

Résumé

Dans [7], nous avions étudié les conditions suffisantes de convergence uniforme presque complète et la vitesse de convergence, d'estimateurs non paramétriques par la méthode du noyau de la densité de la mesure moyenne et de la régression dans le cas d'un processus de Poisson ; cette étude généralise ces résultats à une classe plus large de processus ponctuels, notée F. Pour citer cet article : A. Diakhaby, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 597-602.

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Abstract

Our aim is to generalize some results obtained for a Poisson point process in [7], to a general point process. Those results are in field of complete convergence of two like Parzen-Rosenblatt estimates of density of mean measure function and regression curves. Those estimates are defined from the superposition of n i.i.d. point processes as: fn(x)=1nh∑i=1mKx−Xi(n)h(n)andΨn(x)=∑i=1mYiKx−Xi(n)h(n)∑i=1mKx−Xi(n)h(n), where m is the number of seem generics points of the superposition. We give some sufficient conditions for the convergence of those kernel-like estimators. To cite this article: A. Diakhaby, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 597-602.

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