Model Specification: The Views of Fisher and Neyman, and Later Developments

Abstract

Since Fisher's formulation in 1922 of a framework for theoretical statistics, statistical theory has been concerned primarily with the deriva-tion and properties of suitable statistical procedures on the basis of an assumed statistical model (including sensitivity to deviations from this model). Until relatively recently, the theory has paid little attention to the question of how such a model should be chosen. In the present paper, we consider first what Fisher and Neyman had to say about this problem and in Section 2 survey some contributions statistical theory has made to it. In Section 3 we study a distinction between two types of models (empirical and explanatory) which has been discussed by Neyman, Box, and others. A concluding section considers some lines of further work. Where do probability models come from? To judge by the resounding silence over this question on the part of most statisticians, it seems highly embarrassing. In general, the theoretician is happy to accept that his abstract probability tri-ple (!2, A, P) was found under a gooseberry bush, while the applied statistician's model "just growed". A. P . Dawid (1982) 1. THE VIEWS OF FISHER AND NEYMAN