Goodness-of-fit testing in regression: A finite sample comparison of bootstrap methodology and Khmaladze transformation

Abstract

It is well known that the tests based on the residual empirical process for fitting an error distribution in regression models are not asymptotically distribution free. One either uses a Monte-Carlo method or a bootstrap method to implement them. Another option is to base tests on the Khmaladze transformation of these processes because it renders them asymptotically distribution free. This note compares Monte-Carlo, naive bootstrap, and the smooth bootstrap methods of implementing the Kolmogorov–Smirnov test with the Khmaladze transformed test. We find that the transformed test outperforms the naive and smooth bootstrap methods in preserving the level. The note also includes a power comparison of these tests.