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The “closest” estimates of statistical parameters

Published online by Cambridge University Press:  24 October 2008

E. J. G. Pitman
E. J. G. Pitman
Affiliation:
Hobart, Tasmania
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 33 , Issue 2 , April 1937 , pp. 212 - 222
Copyright
Copyright © Cambridge Philosophical Society 1937

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References

REFERENCES

(1)Pearson, K., “Method of moments and method of maximum likelihood”, Biometrika 28, Parts i and ii (1936), 34–59.CrossRefGoogle Scholar
(2)Pitman, E. J. G., Proc. Camb. Phil. Soc. 32 (1936), 567–79.CrossRefGoogle Scholar