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The uniform consistency of maximum-likelihood estimators

Published online by Cambridge University Press:  24 October 2008

P. A. P. Moran
P. A. P. Moran
Affiliation:
The Australian National University, Canberra
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Extract

Wald(4) proved that under rather weak conditions, maximum-likelihood estimators are consistent. In an earlier paper (3) he had promised to publish conditions under which they are uniformly consistent but he did not do so. As the uniformity of consistence of maximum-likelihood estimators is important in studying the asymptotic power of certain tests, particularly when the true value of the parameter lies on the boundary of the parameter space, the purpose of the present note is to fill this gap. The method of proof follows that of Wald(4) very closely.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 3 , November 1971 , pp. 435 - 439
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Chung, K. L. The strong law of large numbers. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (1951), pp. 341–352. University of California Press.Google Scholar
(2)Kaufmann, S.Asymptotic efficiency of the maximum likelihood estimator. Ann. Inst. Statist. Math. 18 (1966), 155–178.CrossRefGoogle Scholar
(3)Wald, A.Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Amer. Math. Soc. 54 (1943), 426–482.CrossRefGoogle Scholar
(4)Waid, A.Note on the consistency of the maximum likelihood estimate. Ann. Inst. Math. Statist. 20 (1949), 595–601.Google Scholar