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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.
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https://hal.archives-ouvertes.fr/hal-00555752
Contributor : Sophie Laruelle <>
Submitted on : Tuesday, January 17, 2017 - 3:33:15 PM
Last modification on : Monday, December 14, 2020 - 9:45:07 AM
Long-term archiving on: : Tuesday, April 18, 2017 - 3:07:13 PM

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

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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⟩

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