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Randomly Reinforced Urn Designs with Prespecified Allocations

Part of: Sequential methods Limit theorems

Published online by Cambridge University Press:  30 January 2018

Giacomo Aletti ,
Andrea Ghiglietti  and
Anna Maria Paganoni
Giacomo Aletti*
Affiliation:
Università degli Studi di Milano
Andrea Ghiglietti*
Affiliation:
Politecnico di Milano
Anna Maria Paganoni*
Affiliation:
Politecnico di Milano
*
∗ Postal address: Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, via Saldini 50, 20133 Milano, Italy. Email address: giacomo.aletti@unimi.it
∗∗ Postal address: Dipartimento di Matematica“F. Brioschi”, Politecnico di Milano Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
∗∗ Postal address: Dipartimento di Matematica“F. Brioschi”, Politecnico di Milano Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
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Abstract

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We construct a response adaptive design, described in terms of a two-color urn model, targeting fixed asymptotic allocations. We prove asymptotic results for the process of colors generated by the urn and for the process of its compositions. An application of the proposed urn model is presented in an estimation problem context.

Keywords

Reinforced processurn schemesequential clinical trialstochastic process

MSC classification

Primary: 60F15: Strong theorems
Secondary: 62L12: Sequential estimation
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 2 , June 2013 , pp. 486 - 498
Copyright
© Applied Probability Trust 

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