The uniform consistency of maximum-likelihood estimators
- 1 November 1971
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 70 (3) , 435-439
- https://doi.org/10.1017/s0305004100050076
Abstract
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.Keywords
This publication has 5 references indexed in Scilit:
- Asymptotic efficiency of the maximum likelihood estimator)Annals of the Institute of Statistical Mathematics, 1966
- The Strong Law of Large NumbersPublished by University of California Press ,1951
- Note on the Consistency of the Maximum Likelihood EstimateThe Annals of Mathematical Statistics, 1949
- 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