Vitesse de convergence en norme p-intégrale et normalité asymptotique de l'estimateur crible de l'opérateur d'un ARB(1)

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, p∈]1,∞[, and we use Grenander's method of sieves (From U. Grenander, 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).