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


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


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.

Suggested Citation

  • Liu, Aiyi & Wu, Chengqing & Yu, Kai F. & Yuan, Weishi, 2007. "Completeness and unbiased estimation of mean vector in the multivariate group sequential case," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 505-516, March.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:505-516

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    References listed on IDEAS

    1. Weerahandi, Samaradasa, 1987. "Testing Regression Equality with Unequal Variances," Econometrica, Econometric Society, vol. 55(5), pages 1211-1215, September.
    2. Thursby, Jerry G., 1992. "A comparison of several exact and approximate tests for structural shift under heteroscedasticity," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 363-386.
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