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"On Some Optimality Properties of Fisher-Rao Score Function in Testing and Estimation"

Anil K. Bera and Yannis Bilias


First Author :

Anil K. Bera
University of Illinois at Urbana-Champaign
1206 S. Sixth Street, M/C 706
Champaign, IL 61820

Second Author :

Yannis Bilias
University of Cyprus

Abstract :
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.
Manuscript Received : 2000
Manuscript Published : 2000
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