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A Property of Maximum Likelihood Estimators for Invariant Statistical Models

Published online by Cambridge University Press:  20 November 2018

Peter Tan  and
Constantin Drossos
Peter Tan
Affiliation:
Carleton University, Ottawa, Ontario, Canada
Constantin Drossos
Affiliation:
Carleton University, Ottawa, Ontario, Canada
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Abstract

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This paper generalizes some results on pivotal functions of maximum likelihood estimators of location and scale parameters and the related ancillary statistics obtained by Antle and Bain, and Fisher. It shows that the maximum likelihood estimator of the parameter in an invariant statistical model is an essentially equivariant estimator or a transformation variable in a structural model. In the latter case, ancillary statistics in the sense of Fisher used in conjunction with the maximum likelihood estimators can be easily recognized. It is also remarked that the values of maximum likelihood estimators from samples having the same “complexion” are simply related to those of other, perhaps simpler, transformation variables. In the development it also points out the importance of using the correct definition of the likelihood function originally proposed by Fisher.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 3 , August 1975 , pp. 405 - 409
Copyright
Copyright © Canadian Mathematical Society 1975

References

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