The Annals of Statistics

Central Limit Theorems for Doubly Adaptive Biased Coin Designs

Jeffrey R. Eisele and Michael B. Woodroofe

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Abstract

Asymptotic normality of the difference between the number of subjects assigned to a treatment and the desired number to be assigned is established for allocation rules which use Eisele's biased coin design. Subject responses are assumed to be independent random variables from standard exponential families. In the proof, it is shown that the difference may be magnified by appropriate constants so that the magnified difference is nearly a martingale. An application to the Behrens-Fisher problem in the normal case is described briefly.

Article information

Source
Ann. Statist., Volume 23, Number 1 (1995), 234-254.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324465

Digital Object Identifier
doi:10.1214/aos/1176324465

Mathematical Reviews number (MathSciNet)
MR1331666

Zentralblatt MATH identifier
0835.62068

JSTOR
links.jstor.org

Subjects
Primary: 62L05: Sequential design
Secondary: 62E20: Asymptotic distribution theory

Keywords
Exponential families invariance principle martingale central limit theorem sequential allocation

Citation

Eisele, Jeffrey R.; Woodroofe, Michael B. Central Limit Theorems for Doubly Adaptive Biased Coin Designs. Ann. Statist. 23 (1995), no. 1, 234--254. doi:10.1214/aos/1176324465. https://projecteuclid.org/euclid.aos/1176324465


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