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Comptes Rendus Mathématique
Volume 335, n° 9
pages 763-766 (novembre 2002)
Doi : S1631-073X(02)02559-1
Received : 8 Mars 2002 ; 
Sur l'estimation de l'entropie des lois à support dénombrable
On entropy estimation for distributions with countable support
 

Amor Keziou
LSTA, boîte courrier 158, 8A, Université Paris-6, 175, rue du Chevaleret, 75013 Paris, France 

Note présentée par Paul Deheuvels

Résumé

Soit P une loi de probabilité discrète sur un espace infini dénombrable X. On étudie la vitesse de convergence presque sûre de l'estimateur « plug-in » de l'entropie H :=H (P ) de la loi de probabilité inconnue P. On démontre aussi la convergence presque sûre de l'estimateur pour des variables aléatoires stationnaires ergodiques, et pour des variables aléatoires stationnaires -mélangeantes sous une condition faible sur la queue de distribution de la loi P. Pour citer cet article : A. Keziou, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 763-766.

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

Suppose P is a discrete distribution on an infinite countable space X. We study the almost surely convergence rate of the ‘plug-in' estimate of the entropy H :=H (P ) of the arbitrary distribution P. We prove also the consistency of the estimate for ergodic stationary random variables and for -mixing stationary random variables under weak assumptions on the tail of the distribution P. To cite this article: A. Keziou, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 763-766.

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


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