Goodness-of-fit testing for varying-coefficient models

We construct an empirical process-based test to examine the adequacy of varying-coefficient models. A Monte Carlo approach is applied to approximate the null distribution of the test. Due to the use of the Monte Carlo test procedure, beyond the desired features that are shared by the existing empirical process-based tests, our test is self-invariant, which overcomes the difficulty of estimating the variance of the test. Simulations are provided to illustrate our methodology.