Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach

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 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.
Type de document :
Communication dans un congrès
Joint Meeting of the Statistical Society of Canada and the Société Française de Statistique, May 2008, Ottawa, Canada
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https://hal.archives-ouvertes.fr/hal-00325866
Contributeur : Anne Gégout-Petit <>
Soumis le : mardi 30 septembre 2008 - 16:00:06
Dernière modification le : mardi 6 octobre 2015 - 08:38:45

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  • HAL Id : hal-00325866, version 1

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Anne Gégout-Petit, Benoîte De Saporta, Bernard Bercu. Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach. Joint Meeting of the Statistical Society of Canada and the Société Française de Statistique, May 2008, Ottawa, Canada. <hal-00325866>

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