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.

翻译：在众多科学领域中，研究者常关注响应变量Y与协变量向量X之间的关系。为利用特定模型描述其依赖结构，首先需检验给定X条件下Y的条件密度函数是否属于特定参数族。为此，我们提出一种基于Bootstrap的一致性拟合优度检验方法。该检验统计量通过追踪Y的边缘分布函数的非参数估计与半参数估计之间的差异来构建。由于其在原假设下的渐近分布并非分布自由，我们采用参数化Bootstrap方法确定临界值。模拟研究表明，在某些情况下，新方法对参数模型偏离的敏感性优于文献中的其他检验方法。我们还将该方法应用于实际数据集进行验证。