Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach
GÉGOUT-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]
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]
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]
GÉGOUT-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]
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]
BERCU, Bernard
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Communication dans un congrès
This item was published in
Joint Meeting of the Statistical Society of Canada and the Société Française de Statistique, 2008-05-25, Ottawa.
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 <
English Keywords
Bifurcating auto-regression
Tree-indexed times series
Martingales
Least-squares estimator
Almost sure convergence
Convergence rate
Quadratic strong law
Central limit theorem
Origin
Hal imported