Asymptotic analysis for bifurcating autoregressive processes via a martingale approach
BERCU, Bernard
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
DE SAPORTA, Benoîte
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]
GEGOUT-PETIT, Anne
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
BERCU, Bernard
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
DE SAPORTA, Benoîte
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]
GEGOUT-PETIT, Anne
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Langue
en
Article de revue
Ce document a été publié dans
Electronic Journal of Probability. 2009-11-11, vol. 14, n° 87, p. 2492-2526
Institute of Mathematical Statistics (IMS)
Résumé en anglais
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise ...Lire la suite >
We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.< Réduire
Mots clés en anglais
bifurcating autoregressive process
tree-indexed times series
martingales
least squares estimation
almost sure convergence
quadratic strong law
central limit theorem
Origine
Importé de halUnités de recherche