The Annals of Statistics

Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn

Caterina May and Nancy Flournoy

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Abstract

This paper illustrates asymptotic properties for a response-adaptive design generated by a two-color, randomly reinforced urn model. The design considered is optimal in the sense that it assigns patients to the best treatment, with probability converging to one. An approach to show the joint asymptotic normality of the estimators of the mean responses to the treatments is provided in spite of the fact that allocation proportions converge to zero and one. Results on the rate of convergence of the number of patients assigned to each treatment are also obtained. Finally, we study the asymptotic behavior of a suitable test statistic.

Article information

Source
Ann. Statist., Volume 37, Number 2 (2009), 1058-1078.

Dates
First available in Project Euclid: 10 March 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1236693160

Digital Object Identifier
doi:10.1214/08-AOS596

Mathematical Reviews number (MathSciNet)
MR2502661

Zentralblatt MATH identifier
1162.62076

Subjects
Primary: 62L05: Sequential design
Secondary: 60F15: Strong theorems 60F05: Central limit and other weak theorems

Keywords
Generalized Pólya urn adaptive designs asymptotic normality rate of convergence optimal allocation estimation and inference clinical trials ethical allocation testing mean differences treatment allocation two-sample t-test mixing convergence

Citation

May, Caterina; Flournoy, Nancy. Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn. Ann. Statist. 37 (2009), no. 2, 1058--1078. doi:10.1214/08-AOS596. https://projecteuclid.org/euclid.aos/1236693160


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References

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