Weighted discrepancies and maximum likelihood estimation for discrete distributions

Abstract

The paper shows that many estimation methods, including ML, moments, even-points, empirical c.f. and minimum chi-square, can be regarded as scoring procedures using weighted sums of the discrepancies between observed and expected frequencies The nature of the weights is investigated for many classes of distributions; the study of approximations to the weights clarifies the relationships between estimation methods, and also leads to useful formulae for initial values for ML iteration.