Criteria of estimation in large samples

Abstract

The existing criteria of consistency and efficiency of estimation have been examined in the light of recent criticisms and controversies concerning them. A new criterion called uniform first order efficiency which is a better indicator of the performance of an estimator in statistical inference has been introduced. It is, however, pointed out that the anomaly in the earlier criterion of efficiency can be removed by considering consistent estimators which converge to a normal distribution uniformly in compacts of the parameter space. First order efficiency by itself cannot discriminate among a large number of estimation procedures. Therefore, an additional criterion called the second order efficiency has been introduced, which considerably restricts the class of useful estimation procedures and by which several well established estimation procedures could be eliminated in favour of the method of maximum likelihood.