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Note on some properties of maximum likelihood estimates

Published online by Cambridge University Press:  24 October 2008

P. H. Diananda
P. H. Diananda
Affiliation:
Gonville and Caius CollegeCambridge
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Extract

The properties of (1) consistency and (2) asymptotic normality of maximum likelihood estimates of one unknown parameter, for independent observations, have been discussed rigorously by Cramér ((1), p. 500) and Doob (2). These properties were first stated by Fisher (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 4 , October 1949 , pp. 536 - 544
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

(1)Cramér, H.Mathematical Methods of Statistics (Princeton, 1946).Google Scholar
(2)Doob, J. L.Trans. American Math. Soc. 36 (1934), 759.CrossRefGoogle Scholar
(3)Fisher, R. A.Philos. Trans. A, 222 (1921), 309.Google Scholar
(4)Hardy, G. H., Littlewood, J. E. and Pólya, G.Inequalities (Cambridge, 1934), p. 79.Google Scholar
(5)Uspensky, J. V.Introduction to Mathematical Probability (McGraw Hill, 1937), p. 30.Google Scholar