Discrimination among some parametric models

Abstract

SUMMARY Linear models, with errors that follow the distribution of the logarithm of an F statistic, are shown to include a number of common statistical models as special cases. The error model is transformed and reparameterized to induce regular estimation on the boundary with one or both degrees of freedom infinite. This leads to bivariate score tests for normal, extreme value and logistic special cases as well as an evaluation of these models within a more general framework. In particular, the test for normality is found to reduce to the usual tests based on sample skewness and kurtosis. Sample sizes are given for pairwise discrimination among some specific models. Applications are indicated.