Addendum and corrigendum to “Randomized urn models revisited using stochastic approximation”
نویسندگان
چکیده
منابع مشابه
Randomized Urn Models revisited using Stochastic Approximation
This paper presents the link between stochastic approximation and clinical trials based on randomized urn models investigated in [5, 6, 7]. 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 (Central Limit Theorem CLT ) of the no...
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This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2, . . . , n− 1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition a...
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This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2017
ISSN: 1050-5164
DOI: 10.1214/16-aap1242