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Sufficient statistics and minimum variance estimates

Published online by Cambridge University Press:  24 October 2008

C. Radhakrishna Rao
C. Radhakrishna Rao
Affiliation:
King's CollegeCambridge
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Extract

Let the probability density of observations be denoted by φ(x | θ), where x stands for the variables and θ for the parameters. A function t of the observations is called an unbiased estimate of the function ψ(θ) of the parameters if

where dx stands for the product of differentials.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 213 - 218
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

(1)Aitken, A. C. and Silverstone, H.Proc. Roy. Soc. Edinburgh, A, 61 (1942), 186.Google Scholar
(2)Bhattacharya, A.Sankhya, 8 (1947), 1.Google Scholar
(3)Cramér, H.Mathematical methods of statistics (Uppsala, 1945) (reprinted in English, Princeton Univ. Press).Google Scholar
(4)Fisher, R. A.Philos. Trans. A, 222 (1921), 309.Google Scholar
(5)Fisher, R. A.Proc. Roy. Soc. A, 144 (1934), 285.Google Scholar
(6)Koopman, B. O.Trans. American Math. Soc. 39 (1936), 399.CrossRefGoogle Scholar
(7)Rao, C. R.Bull. Calcutta Math. Soc. 37 (1945), 81.Google Scholar
(8)Rao, C. R.Proc. Cambridge Phil. Soc. 43 (1947), 280.CrossRefGoogle Scholar
(9)Widder, D. V.The Laplace transform. (Princeton, 1941).Google Scholar