A Method for Discriminating between Models

Abstract

Summary It is desired to determine which of several alternative models adequately describe the data. The properties of a combined distribution containing the component models as special cases are investigated. Using this distribution, statistics are developed for testing for departures from one model in the direction of another and for testing the hypothesis that all models fit the data equally well. The relationship with other procedures is investigated. Examples are given of the use of the method, especially when there are two component models belonging to separate parametric families.