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The “closest” estimates of statistical parameters

  • E. J. G. Pitman (a1)


A definition of “closer” and “closest” as applied to estimates of statistical parameters is given, and it is shown that we can sometimes prove that estimates properly derived from sufficient statistics are the closest possible.

The scaling of a gamma distribution, and the location and scaling of an exponential distribution and of a rectangular distribution are discussed in detail, and the closest estimates of the parameters obtained.



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(1)Pearson, K., “Method of moments and method of maximum likelihood”, Biometrika 28, Parts i and ii (1936), 3459.
(2)Pitman, E. J. G., Proc. Camb. Phil. Soc. 32 (1936), 567–79.
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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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