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.
Scopus Subject Areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Empirical process
- Monte Carlo approximation
- Varying-coefficient longitudinal model