Testing goodness of fit for the distribution of errors in regression models

Abstract

SUMMARY Asymptotic results are given for the problem of testing goodness of fit for any specified distribution of errors in multiple regression models. In particular, the results apply to the case of testing for normality in standard regression and experimental design models. For a very wide class of goodness of fit statistics, in particular those which depend only on the empirical distribution of the residuals, it is shown that the limiting distributions under the null hypothesis are precisely the same in regression models as in ordinary location-scale models.