On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications

Abstract : We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of any even order converge in the almost sure cental limit theorem for martingales. A conjecture about almost sure upper bounds under wider hypotheses is formulated. The theoretical results are supported by examples borrowed from statistical applications, including linear autoregressive models and branching processes with immigration, for which new asymptotic properties are established on estimation and prediction errors.
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[Research Report] RR-6780, INRIA. 2008, pp.26
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https://hal.inria.fr/inria-00348138
Contributeur : Guy Fayolle <>
Soumis le : mercredi 17 décembre 2008 - 18:51:34
Dernière modification le : samedi 17 septembre 2016 - 01:36:43
Document(s) archivé(s) le : mardi 8 juin 2010 - 17:42:02

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  • HAL Id : inria-00348138, version 1
  • ARXIV : 0812.3528

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Bernard Bercu, Peggy Cénac, Guy Fayolle. On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications. [Research Report] RR-6780, INRIA. 2008, pp.26. <inria-00348138>

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