How ancillary statistics can be Informative

Author

Isfahan, Kashan University, Department of Statistics

Abstract

­­­­Ancillary statistics apparently do not provide any information about the unknown parameter, as their distribution does not depend on the unknown parameter. If a sufficient statistic is also complete, unnecessary information about the sample regarding the unknown parameter is eliminated, and in this case, the completeness of a sufficient statics leads to the greatest compression in the data. In fact, the complete sufficient statistic is independent of any desired ancillary statistic. In this article, it is shown that although ancillary statistics apparently do not provide any information about the parameter, when their joint distribution with a maximum likelihood estimator is considered, a minimal sufficient statistic is obtained. With this approach, lost information in the ancillary statistic is recovered, and ultimately, the ancillary statistic, combined with a maximum likelihood estimator, provides insightful information. It is also demonstrated that by conditioning on the ancillary statistics, there is a guarantee that no information about the parameter will be lost. In this case as well, conditioning on the ancillary statistics will be informative.

Keywords

References

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History

  • Receive Date: 07 August 2017
  • Revise Date: 31 October 2019
  • Accept Date: 08 December 2019
  • Publish Date: 23 August 2019

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