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Comptes Rendus Mathématique
Volume 341, n° 6
pages 369-374 (septembre 2005)
Doi : 10.1016/j.crma.2005.05.009
Received : 3 December 2004 ;  accepted : 3 May 2005
Vitesse de convergence en norme p -intégrale et normalité asymptotique de lʼestimateur crible de lʼopérateur dʼun ARB(1)
Rate of convergence for Sieve estimator of the operator in ARB(1) process
 

Fatiha Rachedi a, b
a Université Aboubekr Belkaïd, département de mathématiques, Tlemcen 13000, Algérie 
b LSTA, université Paris 6, 175, rue du Chevaleret, 75013 Paris, France 

Résumé

Le modèle autorégressif dans un espace de Banach (ARB) permet de représenter des processus à temps continu (voir, par exemple, D. Bosq, Linear Processes in Function Spaces: Theory and Applications, 2000, Springer, p. 150). Dans cette Note, nous considérons lʼestimation, par la méthode des moindres carrés, de lʼopérateur dʼun ARB(1) dans le cas où cet opérateur est strictement p -intégral,  , en utilisant la méthode des cribles de Grenander. Nous montrons la convergence de lʼestimateur crible et sa normalité asymptotique. Pour citer cet article : F. Rachedi, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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

The autoregressive model in a Banach space (ARB) allows to represent many continuous time processes used in practice (see, for example, D. Bosq, Linear Processes in Function Spaces: Theory and Applications, 2000, Springer, p. 150). In this Note we study an estimator of the operator in ARB(1) by the least squares method, when the operator is strictly p -integral,  , and we use Grenanderʼs method of sieves (From U. Grenander, Abstract Inference, Wiley, 1981). We show consistency of the sieve estimator and we derive a central limit theorem for this estimator. To cite this article: F. Rachedi, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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


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