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February, 1995 Central Limit Theorems for Doubly Adaptive Biased Coin Designs
Jeffrey R. Eisele, Michael B. Woodroofe
Ann. Statist. 23(1): 234-254 (February, 1995). DOI: 10.1214/aos/1176324465


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.


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Jeffrey R. Eisele. Michael B. Woodroofe. "Central Limit Theorems for Doubly Adaptive Biased Coin Designs." Ann. Statist. 23 (1) 234 - 254, February, 1995.


Published: February, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0835.62068
MathSciNet: MR1331666
Digital Object Identifier: 10.1214/aos/1176324465

Primary: 62L05
Secondary: 62E20

Keywords: exponential families , invariance principle , martingale central limit theorem , Sequential allocation

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 1 • February, 1995
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