Maximum-likelihood estimation in non-standard conditions
- 1 November 1971
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 70 (3) , 441-450
- https://doi.org/10.1017/s0305004100050088
Abstract
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.Keywords
This publication has 4 references indexed in Scilit:
- The uniform consistency of maximum-likelihood estimatorsMathematical Proceedings of the Cambridge Philosophical Society, 1971
- On the Estimation of Parameters Restricted by InequalitiesThe Annals of Mathematical Statistics, 1958
- Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is LargeTransactions of the American Mathematical Society, 1943
- Tests of statistical hypotheses concerning several parameters when the number of observations is largeTransactions of the American Mathematical Society, 1943