JSM 2004 - Toronto

Abstract #300461

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Activity Number: 311
Type: Contributed
Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #300461
Title: Unbiased Estimation Following a Group Sequential Test for Distributions in the Exponential Family
Author(s): Aiyi Liu *+ and Jack Hall and Kai F. Yu and Chengqing Wu
Companies: National Institutes of Health and University of Rochester Medical Center and National Institutes of Health and National Institutes of Health
Address: DESPR/NICHD/NIH/DHHS, Rockville, MD, 20852,
Keywords: clinical trials ; completeness ; Laplace transform ; minimum variance ; truncation-adaptation
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; moreover, this estimator is identical to one based on the Rao-Blackwell theorem. When completeness fails, we show that the uniformly minimum-variance unbiased estimator may not exist or otherwise possess undesirable performance, thus claiming the optimality of the Rao-Blackwell estimator, regardless of the completeness of the sufficient statistics. The results have potential application in clinical trials and other fields.

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