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Sufficient Statistics and Orthogonal Parameters

Published online by Cambridge University Press:  24 October 2008

Ann F. S. Mitchell
Ann F. S. Mitchell
Affiliation:
The Statistical LaboratoryCambridge
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Extract

Let be, for a set of n real continuous parameters the probability density function of a random variable x with respect to a σ-finite measure μ on a σ-algebra of subsets of the sample space . If x; is a continuous random variable, μ will be Lebesgue measure on the Borel sets of a Euclidean sample space and, if x is discrete, μ will be counting measure on the class of all sets of a countable sample space. The parameters αi are said to be orthogonal (Jeffreys (3), pp. 158,184) if .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 326 - 337
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

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