inria-00348138, version 1
On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications
Bernard Bercu
1, 2Peggy Cénac a, 3Guy Fayolle
b, 4
N° RR-6780 (2008)
Résumé : 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.
- a – Université de Bourgogne
- b – INRIA
- 1 : Institut de Mathématiques de Bordeaux (IMB)
- CNRS : FR2254 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
- 2 : CQFD (INRIA Bordeaux - Sud-Ouest)
- INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR5251
- 3 : Institut de Mathématiques de Bourgogne (IMB)
- CNRS : UMR5584 – Université de Bourgogne
- 4 : IMARA (INRIA Rocquencourt)
- INRIA
- Domaine : Mathématiques/Probabilités
- Mots-clés : Almost sure central limit theorem – vector martingale – moment – stochastic regression
- Référence interne : RR-6780
- inria-00348138, version 1
- http://hal.inria.fr/inria-00348138
- oai:hal.inria.fr:inria-00348138
- Contributeur : Guy Fayolle
- Soumis le : Mercredi 17 Décembre 2008, 18:51:34
- Dernière modification le : Vendredi 19 Décembre 2008, 11:21:42
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