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\footnotesize
\noindent Statistica Sinica {\bf 16}(2006), 165-181

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\centerline{\large\bf ESTIMATION FOLLOWING A GROUP SEQUENTIAL TEST}
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\centerline{\large\bf FOR DISTRIBUTIONS IN THE}
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\centerline{\large\bf ONE-PARAMETER EXPONENTIAL FAMILY}
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\author{Aiyi Liu$^{1}$, W.  J. Hall$^{2}$, Kai F. Yu$^{1}$ and Chengqing Wu$^{1, 3}$}
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\centerline{\it $^{1}$National Institute of Child Health and Human Development,}
\centerline{\it $^{2}$University of Rochester
and $^{3}$University of Science and Technology of China}
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\begin{quotation}
\noindent {\it Abstract:}
 We consider unbiased estimation following
a group sequential test for distributions in a one-parameter
exponential family. We show that, for an estimable parameter
function, there exists uniquely an unbiased estimator depending on
the sufficient statistic and based on the truncation-adaptation
criterion (Liu and Hall (1999)); moreover, this estimator is
identical to one based on the Rao-Blackwell method. When
completeness fails, we show that the uniformly minimum-variance
unbiased estimator may not exist or might possess undesirable
performance. A Phase-II clinical trial application with
exponentially distributed responses is included.\par
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\noindent {\it Key words and phrases:}
Clinical trials,
completeness, Laplace transform, minimum variance,
truncation-adaptation, unbiased estimation.\par
\end{quotation}

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