Testing the simplifying assumption in high-dimensional vine copulas is a difficult task. Tests must be based on estimated observations and check constraints on high-dimensional distributions. So far, corresponding tests have been limited to single conditional copulas with a low-dimensional set of conditioning variables. We propose a novel testing procedure that is computationally feasible for high-dimensional data sets and that exhibits a power that decreases only slightly with the dimension. By discretizing the support of the conditioning variables and incorporating a penalty in the test statistic, we mitigate the curse of dimensionality by looking for the possibly strongest deviation from the simplifying assumption. The use of a decision tree renders the test computationally feasible for large dimensions. We derive the asymptotic distribution of the test and analyze its finite sample performance in an extensive simulation study. An application of the test to four real data sets is provided.
翻译:测试必须基于估计的观测结果和对高维分布的检查限制。 到目前为止,相应的测试仅限于单一的有条件的相阳管,且有一套低维的调节变量。 我们提议了一个新颖的测试程序,该程序在计算上对高维数据集来说是可行的,并且显示的能量仅与尺寸略有下降。 通过对调控变量的支持进行分解,并在测试统计中加入一个罚则,我们通过寻找可能最强烈的偏离,来减轻对维度的诅咒。 使用决定树使得测试在计算上可以适用于大维。 我们从广泛的模拟研究中得出测试的无药性分布,并分析其有限的样本性能。 我们提供了对四个真实数据集的测试应用。