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Biometrika 1999 86(1):71-78; doi:10.1093/biomet/86.1.71
© 1999 by Biometrika Trust
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Unbiased estimation following a group sequential test

A LiuA1 and WJ HallA2

A1 Department of Biostatistics and Epidemiology, St Jude Children's Research Hospital, Memphis, TN 38134, USA aiyi.liu@stjude.org A2 Department of Biostatistics, University of Rochester Medical Center, Rochester, NY 14642-8630, USA hall@bst.rochester.edu

It is shown that, in a group sequential test about the drift {theta} of a Brownian motion X(t) stopped at time T, the sufficient statistic (T, X(T)) is not complete for {theta}. There exist infinitely many unbiased estimators of {theta} and none has uniformly minimum variance. A truncation-adaptable criterion is proposed, and the uniformly-minimum-variance estimator among all truncation-adaptable unbiased estimators is found. This estimator is identical to estimators of Ferebee (1983) and Emerson & Fleming (1990).

Keywords:Brownian motion; Truncation-adaptation.


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