Analyse asymptotique des processus autorégressifs de bifurcation par des méthodes de martingales.
GÉGOUT-PETIT, Anne
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
DE SAPORTA, Benoîte
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]
BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
GÉGOUT-PETIT, Anne
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
DE SAPORTA, Benoîte
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]
BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Language
fr
Communication dans un congrès
This item was published in
Journées MAS de la SMAI, 2008-08-28, Rennes.
English Abstract
We study the least-square (LS) estimator of the unknown parameters of a bifurcating auto-regressive process (BAR). Under very weak assumptions on the noise sequence (namely conditional pair-wise independence and moments ...Read more >
We study the least-square (LS) estimator of the unknown parameters of a bifurcating auto-regressive process (BAR). Under very weak assumptions on the noise sequence (namely conditional pair-wise independence and moments of order $4$), we derive a precise rate of convergence for the LS estimator, as well as a quadratic strong law and a central limit theorem. Our main tool is martingale theory. However, standard results do not apply directly, as the martingales involved here have a special form and an exponential growth rate.Read less <
Keywords
Processus autoregressifs de bifurcation
séries temporelles indexées par un arbre
Martingales
Estimateur des moindres carrés
Convergence presque sûre
Loi forte quadratique
Théorème Cenytral Limite
Origin
Hal imported