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Comptes Rendus Mathématique
Volume 344, n° 8
pages 515-518 (avril 2007)
Doi : 10.1016/j.crma.2007.02.017
Received : 20 June 2006 ;  accepted : 26 February 2007
Vitesses de convergence dans la loi forte des grands nombres et dans lʼestimation de la densité pour des variables aléatoires associées
Convergence rates in the law of large numbers and for density estimation for associated random variables
 

Lahcen Douge
L.S.T.A., Université Paris 6, 175, rue du Chevaleret, 75013 Paris, France 

Résumé

Nous considérons un processus stationnaire associé  . Nous établissons une nouvelle inégalité exponentielle et nous déduisons une vitesse de convergence dans la loi forte des grands nombres. Pour ce type de processus une vitesse de convergence presque sûre uniforme sur les ensembles compacts de lʼestimateur à noyau de la fonction de densité est également établie. Pour citer cet article : L. Douge, C. R. Acad. Sci. Paris, Ser. I 344 (2007).

The full text of this article is available in PDF format.
Abstract

Let   be a stationary associated random process. We give a new exponential inequality and derive a rate of convergence for the law of large numbers. For this type of process, a uniform almost sure rate of convergence over compact sets for the kernel density estimator is also given. To cite this article: L. Douge, C. R. Acad. Sci. Paris, Ser. I 344 (2007).

The full text of this article is available in PDF format.


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