Moment-type estimation in the exponential family
Roger R. Davidson, Daniel L. Daniel · Communications in Statistics · 1974
Some aspects of the Pearson-Fisher controversy concerning the method of moments and the method of maximum likelihood are reviewed. In the multiparameter exponential family, a modification of the method of moments which requires the estimators to be functions of the minimal sufficient statistic is discussed It is shown that these modified estimators are in fact the maximum likelihood estimators.Although the mathematics underlying the result is widely available in the literature, the authors have not seen it stated in the present context.