A permutation approach to goodness-of-fit testing inregression models /

Model checking plays an important role in parametric regression asmodel misspecification seriously affects the validity and efficiency ofregression analysis. Model checks can be performed by constructingan empirical process from the model’s fitted values and residuals.Due to a complex covariance function of the process obtaining theexact distribution of the test statistic is, however, intractable. Sev-eral solutions to overcome this have been proposed. It was shownthat the simulation and bootstrap-based approaches are asymptoti-cally valid, however, we show by using simulations that the rate ofconvergence can be slow. We, therefore, propose to estimate thenull distribution by using a novel permutation-based procedure. Weprove, under some mild assumptions, that this yields consistent testsunder the null and some alternative hypotheses. Small sample prop-erties of the proposed approach are studied in an extensive MonteCarlo simulation study and real data illustration is also provided.