Randomized Urn Models revisited using Stochastic Approximation

Abstract : This paper presents the link between stochastic approximation and clinical trials based on randomized urn models investigated in Bai and Hu (1999,2005) and Bai, Hu and Shen (2002). We reformulate the dynamics of both the urn composition and the assigned treatments as standard stochastic approximation (SA) algorithms with remainder. Then, we derive the a.s. convergence and the asymptotic normality (CLT) of the normalized procedure under less stringent assumptions by calling upon the ODE and SDE methods. As a second step, we investigate a more involved family of models, known as multi-arm clinical trials, where the urn updating depends on the past performances of the treatments. By increasing the dimension of the state vector, our SA approach provides this time a new asymptotic normality result.
Type de document :
Article dans une revue
Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2013, 23 (4), pp.1409-1436
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00555752
Contributeur : Sophie Laruelle <>
Soumis le : mardi 17 janvier 2017 - 15:33:15
Dernière modification le : jeudi 27 avril 2017 - 09:46:40
Document(s) archivé(s) le : mardi 18 avril 2017 - 15:07:13

Fichiers

Urnes6.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00555752, version 6
  • ARXIV : 1101.2786

Collections

Citation

Sophie Laruelle, Gilles Pagès. Randomized Urn Models revisited using Stochastic Approximation. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2013, 23 (4), pp.1409-1436. <hal-00555752v6>

Partager

Métriques

Consultations de
la notice

75

Téléchargements du document

11