Bootstrap-based goodness-of-fit test for parametric families of conditional distributions

In various scientific fields, researchers are interested in exploring the relationship between some response variable Y and a vector of covariates X. In order to make use of a specific model for the dependence structure, it first has to be checked whether the conditional density function of Y given X fits into a given parametric family. We propose a consistent bootstrap-based goodness-of-fit test for this purpose. The test statistic traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function of Y. As its asymptotic null distribution is not distribution-free, a parametric bootstrap method is used to determine the critical value. A simulation study shows that, in some cases, the new method is more sensitive to deviations from the parametric model than other tests found in the literature. We also apply our method to real-world datasets.