On the Use of Minimum Chi-Square Estimation

The method of maximum likelihood estimation is widely used and its sovereignty has been questioned recently by Berkson (1980) who argues that minimum chi-square and not maximum likelihood is the basic principle of statistical inference. In any application a wide range of estimators exist that would be classed by Berkson as minimum chi-square estimators whilst in the literature the definition of such a class is not without ambiguity. This paper reviews some aspects of the history and background to this ambiguity and argues in favour of a wider use of pure minimum chi-square estimation. The usefulness of this method in the wider context of statistical modelling is illustrated by a consideration of the appropriateness of a geometric distribution to some bus passenger frequency data.