GÉGOUT-PETIT, Anne; DE SAPORTA, Benoîte; BERCU, Bernard

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GÉGOUT-PETIT, Anne
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]

BERCU, Bernard
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]

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Communication dans un congrès

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Joint Meeting of the Statistical Society of Canada and the Société Française de Statistique, 2008-05-25, Ottawa.

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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.< Leer menos

Palabras clave en inglés

Bifurcating auto-regression

Tree-indexed times series

Martingales

Least-squares estimator

Almost sure convergence

Convergence rate

Quadratic strong law

Central limit theorem

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Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach

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