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Sufficient statistics and intrinsic accuracy

  • E. J. G. Pitman (a1)
Extract

It is proved that if there exists a sufficient statistic for the estimation of an unknown parameter of a population, the frequency function of the population must be of a certain type.

It is shown that some modification of previous theory of the intrinsic accuracy of statistics is necessary when the range of the population sampled is a function of the parameter to be estimated.

Finally, the theory is extended to sufficient sets of statistics, i.e. sets of statistics which together contain all the information provided by a sample about an unknown parameter.

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References
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(1)Fisher, R. A., Phil. Trans. A, 222 (1922), 309.
(2)Fisher, R. A., Proc. Camb. Phil. Soc. 22 (1925), 700.
(3)Fisher, R. A., Proc. Roy. Soc. A, 144 (1933), 285.
(4)Elderton, W. Palin, Frequency Curves and Correlation (1906).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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