We propose a test procedure to compare simultaneously $K$ copulas, with $K \geq 2$. The $K$ observed populations can be paired. The test statistic is based on the differences between orthogonal projection coefficients associated to the density copulas, that we called {\it copula coefficients}. The procedure is data driven and we obtain a chi-square asymptotic distribution of the test statistic under the null. We illustrate our procedure via numerical studies and through two real datasets. Eventually, a clustering algorithm is deduced from the $K$-sample test and its performances are illustrated in a simulation experiment.
翻译:我们提出一个测试程序,将千兆瓦与千兆瓦(KK)和千兆瓦(Geq 2)进行同时比较。观察到的人口可以对齐。测试统计数据基于与密度千兆瓦(我们称之为“千兆瓦系数”)相关的正方位预测系数之间的差异。测试程序是数据驱动的,我们在无效数据下获得测试统计数据的“无孔径”分布。我们通过数字研究和两个真实数据集来说明我们的程序。最终,从“千兆瓦”抽样测试中推导出一个组合算法,并在模拟实验中展示其性能。