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Completeness and unbiased estimation of mean vector in the multivariate group sequential case

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  • Liu, Aiyi
  • Wu, Chengqing
  • Yu, Kai F.
  • Yuan, Weishi
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    Abstract

    We consider estimation after a group sequential test about a multivariate normal mean, such as a [chi]2 test or a sequential version of the Bonferroni procedure. We derive the density function of the sufficient statistics and show that the sample mean remains to be the maximum likelihood estimator but is no longer unbiased. We propose an alternative Rao-Blackwell type unbiased estimator. We show that the family of distributions of the sufficient statistic is not complete, and there exist infinitely many unbiased estimators of the mean vector and none has uniformly minimum variance. However, when restricted to truncation-adaptable statistics, completeness holds and the Rao-Blackwell estimator has uniformly minimum variance.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 3 (March)
    Pages: 505-516

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:505-516

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    Related research

    Keywords: Bias Interim analysis Mean squared error Medical trials Minimum variance Multiple endpoints Restricted completeness Truncation-adaptation;

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