Cramer-von Mises statistics for discrete distributions
John Joseph Spinelli · Summit (Simon Fraser University) · 1994
Testing the hypothesis that a sample of data arises from a specified distribution, called goodness-of-fit, is an important problem in statistics.To date most of the research has focussed on continuous distributions.Tests based on the empirical distribution function, and in particular the Cramfir-von Mises statistics, have been shown to be powerful tests of fit for such distributions.Discrete distributions are important to many areas of research, and often arise with medical data.In this thesis, the Cram&-von Mises statistics are developed for the Binomial and Poisson distributions.The asymptotic distributions of the test statistics are derived, and the distributions for finite samples are obtained by Monte Carlo methods.They are shown to converge rapidly to their asymptotic distributions.Power studies are given to compare the new tests t o other tests which have been proposed for these distributions.Another important research area is testing goodness-of-fit for regression models.Here the hypothesis is that the data are from a specified distribution, but with mean value dependent on a set of covariates.The regression model for normally distributed observations has been extensively studied.In this thesis?several analogues to the Cram&-von Mises statistics are derived for testing goodness-of-fit for discrete regression models.Asymptotic theory is given and the properties of the test statistics are examined.iii Offset + Age + Exposure. . . . . . . . .