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An extension of the Pitman–Koopman Theorem

Published online by Cambridge University Press:  24 October 2008

Harold Jeffreys
Harold Jeffreys
Affiliation:
St John's CollegeCambridge
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Abstract

The theorems of Pitman and Koopman on laws of chance that yield sufficient statistics are extended to laws where the parameter or the observable, or both, may admit only a discrete set of values. The method depends on making changes, not necessarily small, within the values permitted for the variables, but it is still necessary to assume a solubility condition.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 4 , October 1960 , pp. 393 - 395
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

REFERENCES

(1)Pitman, E. J. G.Proc. Camb. Phil. Soc. 32 (1936), 567–79.CrossRefGoogle Scholar
(2)Koopman, B. O.Trans. Amer. Math. Soc. 39 (1936), 399–409.CrossRefGoogle Scholar