On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications - Université de Bourgogne Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2008

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

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.
Fichier principal
Vignette du fichier
RR-6780.pdf (263.36 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

inria-00348138 , version 1 (17-12-2008)

Identifiants

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

Citer

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⟩
343 Consultations
426 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More