On some optimality properties of fisher-rao score function in testing and estimation

Anil K. Bera, Yannis Bilias

Research output: Contribution to journalConference articlepeer-review


The score function is associated with some optimality features in statistical inference. This review article looks on the central role of the score in testing and estimation. The maximization of the power in testing and the quest for efficiency in estimation lead to score as a guiding principle. In hypothesis testing, the locally most powerful test statistic is the score test or a transformation of it. In estimation, the optimal estimating function is the score. The same link can be made in the case of nuisance parameters: the optimal test function should have maximum correlation with the score of the parameter of primary interest. We complement this result by showing that the same criterion should be satisfied in the estimation problem as well.

Original languageEnglish (US)
Pages (from-to)1533-1559
Number of pages27
JournalCommunications in Statistics - Theory and Methods
Issue number8-9
StatePublished - 2001
EventStatistics Reflections on the Past and Visions for the Future-International Conference in Honor of Prof. C.R. Rao on the Occasion of His 80th Birthday- - San Antonio, TX, United States
Duration: Mar 16 2000Mar 19 2000


  • Efficiency
  • Efficient method of moment
  • Estimating function
  • Locally most powerful test
  • Rao's score test
  • Score function

ASJC Scopus subject areas

  • Statistics and Probability


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