Abstract
We consider a Brownian motion X(t) with drift θ and various linear stopping boundaries, including boundaries popular for sequential testing. We show that the stopping time T and the observed value X(T) are jointly complete for the drift. We then derive the UMVUE of the drift and of some functions of the drift, including the variance of the drift estimate. The estimates are also truncation-adaptable, with uniformly minimum variance among such estimates.
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