In this paper, we introduce a consistent goodness-of-fit test for distributional regression. The test statistic is based on a process that 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 critical values. Empirical results suggest that, in certain scenarios, the test outperforms existing specification tests by achieving a higher power and thereby offering greater sensitivity to deviations from the assumed parametric distribution family. Notably, the proposed test does not involve any hyperparameters and can easily be applied to individual datasets using the gofreg-package in R.

翻译：本文提出了一种用于分布回归的一致性拟合优度检验方法。该检验统计量基于一个追踪Y的边缘分布函数的非参数估计与半参数估计之间差异的过程。由于其在原假设下的渐近分布并非分布无关，我们采用参数化Bootstrap方法来确定临界值。实证结果表明，在某些场景下，该检验通过获得更高的检验功效，在检测偏离假定参数分布族时表现出比现有设定检验更优的性能，从而提供更强的敏感性。值得注意的是，所提出的检验不涉及任何超参数，且可通过R语言中的gofreg包轻松应用于独立数据集。