Randomized urn models revisited using stochastic approximation

DOI10.1214/12-AAP875zbMath1429.62360arXiv1101.2786MaRDI QIDQ363849

Sophie Laruelle, Gilles Pagès

Publication date: 5 September 2013

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.2786

zbMATH Keywords

asymptotic normalitystochastic approximationstrong consistencyadaptive asset allocationextended Pólya urn modelsmulti-arm clinical trialsnonhomogeneous generating matrix

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Asymptotic distribution theory in statistics (62E20) Applications of statistics to biology and medical sciences; meta analysis (62P10) Stochastic approximation (62L20) Sequential statistical design (62L05)

Related Items (28)

Interacting urns on a finite directed graph ⋮ Interacting generalized Friedman's urn systems ⋮ Generalized rescaled Pólya urn and its statistical application ⋮ The rescaled Pólya urn: local reinforcement and chi-squared goodness-of-fit test ⋮ Approximating the operating characteristics of Bayesian uncertainty directed trial designs ⋮ A Finite Memory Interacting Pólya Contagion Network and Its Approximating Dynamical Systems ⋮ Stochastic approximation on noncompact measure spaces and application to measure-valued Pólya processes ⋮ Nonlinear unbalanced urn models via stochastic approximation ⋮ A generalized urn with multiple drawing and random addition ⋮ Azuma-Hoeffding bounds for a class of urn models ⋮ Interacting nonlinear reinforced stochastic processes: Synchronization or non-synchronization ⋮ Barabási-Albert random graph with multiple type edges and perturbation ⋮ Synchronization of reinforced stochastic processes with a network-based interaction ⋮ Pólya urns with immigration at random times ⋮ Convergence in models with bounded expected relative hazard rates ⋮ Strong convergence of infinite color balanced urns under uniform ergodicity ⋮ Negatively reinforced balanced urn schemes ⋮ On a notion of partially conditionally identically distributed sequences ⋮ Nonparametric covariate-adjusted response-adaptive design based on a functional urn model ⋮ An urn model to construct an efficient test procedure for response adaptive designs ⋮ Nonlinear randomized urn models: a stochastic approximation viewpoint ⋮ Multiple drawing multi-colour urns by stochastic approximation ⋮ Interacting reinforced stochastic processes: statistical inference based on the weighted empirical means ⋮ Linear de-preferential urn models ⋮ Networks of reinforced stochastic processes: asymptotics for the empirical means ⋮ Stochastic approximation with random step sizes and urn models with random replacement matrices having finite mean ⋮ Unbalanced multi-drawing urn with random addition matrix ⋮ A new approach to Pólya urn schemes and its infinite color generalization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Martingale functional central limit theorems for a generalized Pólya urn
• An algebraic approach to Pólya processes
• Stochastic approximation and modern model-based designs for dose-finding clinical trials
• Approximation gaussienne d'algorithmes stochastiques à dynamique markovienne. (Gaussian approximation of stochastic algorithms)
• Stochastic approximation methods for constrained and unconstrained systems
• The generalized Polya's urn design for sequential medical trials
• Central limit theorems for urn models
• Asymptotic theorems for urn models with nonhomogeneous generating matrices
• An adaptive design for multi-arm clinical trials
• Asymptotics in randomized urn models
• When can the two-armed bandit algorithm be trusted?
• Stochastic algorithms
• Functional limit theorems for multitype branching processes and generalized Pólya urns.
• Asymptotic Normality in the Generalized Polya–Eggenberger Urn Model, with an Application to Computer Data Structures
• Convergence of stochastic algorithms: from the Kushner–Clark theorem to the Lyapounov functional method
• A randomized play-the-winner design for multi-arm clinical trials
• Bernard Friedman's Urn
• Embedding of Urn Schemes into Continuous Time Markov Branching Processes and Related Limit Theorems

This page was built for publication: Randomized urn models revisited using stochastic approximation