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Sufficiency for multinomial and transition probabilities

Published online by Cambridge University Press:  14 July 2016

Eve Bofinger
Eve Bofinger*
Affiliation:
University of Sydney
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Extract

Gani (1955) finds the form of the multinomial probabilities which admit a sufficient estimator for the single parameter θ to be where λ θ is a positive function of θ, the Ki, are constants and the αi are nonnegative constants.

Type
Short Communications
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 470 - 474
Copyright
Copyright © Applied Probability Trust 

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References

Bhat, B. R. and Gani, J. (1960) A note on sufficiency in regular Markov chains. Biometrika 47, 452–457.CrossRefGoogle Scholar
Gani, J. (1955) Some theorems and sufficiency conditions for the maximum likelihood estimator of an unknown parameter in a simple Markov chain. Biometrika 42, 342–359. Corrigendum: Biometrika (1956) 43, 497-498.CrossRefGoogle Scholar
Gani, J. (1956) Sufficiency conditions in regular Markov chains and certain random walks. Biometrika 43, 276–284.Google Scholar