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Maximum-likelihood estimation in non-standard conditions

Published online by Cambridge University Press:  24 October 2008

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

Extract

The origin of the present paper is the desire to study the asymptotic behaviour of certain tests of significance which can be based on maximum-likelihood estimators. The standard theory of such problems (e.g. Wald(4)) assumes, sometimes tacitly, that the parameter point corresponding to the null hypothesis lies inside an open set in the parameter space. Here we wish to study what happens when the true parameter point, in estimation problems, lies on the boundary of the parameter space.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

(1)Brunk, H. D.On the estimation of parameters restricted by inequalities. Ann. Math. Statist. 29 (1958), 437454.CrossRefGoogle Scholar
(2)Mirsky, L.An Introduction to Linear Algebra. (Oxford University Press, 1955.)Google Scholar
(3)Moran, P. A. P.The uniform consistency of maximum-likelihood estimators. Proc. Cambridge Philos. Soc. 70 (1971), 435439.CrossRefGoogle Scholar
(4)Wald, A.Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Amer. Math. Soc. 54 (1943), 426482.CrossRefGoogle Scholar
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