The Annals of Applied Probability

Asymptotics in randomized urn models

Zhi-Dong Bai and Feifang Hu

Full-text: Open access

Abstract

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 and the patient allocation under general assumptions on random generating matrices which determine how balls are added to the urn. Also we obtain explicit forms of the asymptotic variance–covariance matrices of both the urn composition and the patient allocation. The conditions on the nonhomogeneity of generating matrices are mild and widely satisfied in applications. Several applications are also discussed.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 1B (2005), 914-940.

Dates
First available in Project Euclid: 1 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1107271672

Digital Object Identifier
doi:10.1214/105051604000000774

Mathematical Reviews number (MathSciNet)
MR2114994

Zentralblatt MATH identifier
1059.62111

Subjects
Primary: 62E20: Asymptotic distribution theory 62L05: Sequential design
Secondary: 62F12: Asymptotic properties of estimators

Keywords
Asymptotic normality extended Pólya’s urn models generalized Friedman’s urn model martingale nonhomogeneous generating matrix response-adaptive designs strong consistency

Citation

Bai, Zhi-Dong; Hu, Feifang. Asymptotics in randomized urn models. Ann. Appl. Probab. 15 (2005), no. 1B, 914--940. doi:10.1214/105051604000000774. https://projecteuclid.org/euclid.aoap/1107271672


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