The uniform consistency of maximum-likelihood estimators

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.