A goodness-of-fit test for a varying-coefficients model in longitudinal studies

In this paper, we construct an empirical process-based test to examine the adequacy of a varying-coefficient model. A Monte Carlo approach is applied to approximate the null distribution of the test. Beyond the desired features that are shared by the existing empirical process-based tests, the Monte Carlo approximation makes the test self-invariant such that studentisation for the test statistic is not needed. Thus, the variance of residuals, as a studentising constant that is model dependent and may deteriorate the power of test, is no need to estimate. Simulations and an example are provided to illustrate our methodology.