Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T07:35:40.347Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum-likelihood estimation in non-standard conditions

Published online by Cambridge University Press:  24 October 2008

P. A. P. Moran
P. A. P. Moran
Affiliation:
The Australian National University, Canberra
Get access Rights & Permissions [Opens in a new window]

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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 3 , November 1971 , pp. 441 - 450
Copyright
Copyright © Cambridge Philosophical Society 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Brunk, H. D.On the estimation of parameters restricted by inequalities. Ann. Math. Statist. 29 (1958), 437–454.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), 435–439.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), 426–482.CrossRefGoogle Scholar