Fisher and the Method of Moments

Abstract

The introduction of the method of maximum likelihood by R.A. Fisher offered statisticians a procedure for parameter estimation and some related optimality criteria. The principal tool that had been available previously was the method of moments, developed by Karl Pearson some twenty years earlier. Fisher directly attacked the method of moments in much of his work, and attempted to show the superiority of his likelihood techniques. While Fisher’s views prevailed, the fact that the method of maximum likelihood (ML) and the method of moments (MM) were concerned, in part, with different questions belies any claim to actual superiority of one over the other. This lecture presents a comparison of the two methods and the goals of each. In it we review and summarize Pearson’s work and discuss some of Fisher’s criticisms. Many of the other presentations in this volume contain related discussions.