Empirical processes based on regression residuals: Theory and application

The problem of testing goodness-of-fit when fitting linear regression models is approached in this thesis through a careful study of the weak convergence properties of the empirical processes based on regression residuals. For normal theory linear regression models, the effect of estimating regression parameters and the effect of estimating the standard deviation of the error distribution are shown to be separable, and are each identified. Also identified is the effect of the Box-Cox transformation on estimation of regression parameters and error standard deviation. The weak convergence properties established here cover two different situations: (1) the number of regression parameters is fixed finite; (2) the number of regression parameters increases as sample size increases.;When the error distribution is not normal, a group of contiguous alternatives are studied in detail, and weak convergence properties of residual empirical processes under these contiguous alternatives are obtained.;Applications of the above mentioned weak convergence properties are sought in three areas: (a) testing overall goodness-of-fit when fitting linear regression models; (b) testing overall goodness-of-fit for Box-Cox transformations; and (c) testing composite goodness-of-fit hypotheses for continuous distributions.;Proposals are made to extend the basic ideas of EDF tests to the areas of generalized linear models (GLIM) and transform-both-sides (TBS) models.