Residuals based Kolmogorov-Smirnov and Cramér-von Mises tests for varying coefficient models

In this article, the problem of estimating the model error distribution in a heteroscedastic varying coefficient regression model is considered. A residual-based estimator of the model error distribution is proposed, associated with its asymptotic results. Furthermore, the application of estimated error distribution for testing whether some varying coefficient components are constants or not is investigated. Test statistics based on the Kolmogorov-Smirnov and Cramér-von Mises type functionals of the estimated model error distribution are used to check the null hypothesis. A bootstrap procedure is further proposed to calculate the critical values. Simulation studies are conducted to demonstrate the performance of the proposed test statistics.