Efron's Conjecture on Vulnerability to Bias in a Method for Balancing Sequential Trials
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Operations, Information and Decisions Papers
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balanced experiment
biased coin design
covariance matrix
maximum eigenvalue
sequential trial
Biometry
Other Mathematics
biased coin design
covariance matrix
maximum eigenvalue
sequential trial
Biometry
Other Mathematics
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Steele, J. Michael
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Abstract
Efron (1971) proposed a method for sequential assignment to treatments or control which is in many ways superior to traditional procedures. To analyse the method's susceptibility to accidental bias a criterion concerning the maximum eigenvalue of a fundamental covariance matrix was introduced. On the basis of numerical evidence, Efron conjectured an explicit formula for this eigenvalue. This note gives a proof of that conjecture.
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1980
Journal title
Biometrika