Unbiased estimation following a group sequential test
- 1 March 1999
- journal article
- research article
- Published by Oxford University Press (OUP) in Biometrika
- Vol. 86 (1) , 71-78
- https://doi.org/10.1093/biomet/86.1.71
Abstract
It is shown that, in a group sequential test about the drift θ of a Brownian motion Χ(t) stopped at time Τ, the sufficient statistic (Τ, Χ(Τ)) is not complete for θ. There exist infinitely many unbiased estimators of θ 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.Keywords
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