Visualization and assessment of copula structures are crucial for accurately understanding and modeling the dependencies in multivariate data analysis. In this paper, we introduce an innovative method that employs functional boxplots and rank-based testing procedures to evaluate copula symmetry. This approach is specifically designed to assess key characteristics such as reflection symmetry, radial symmetry, and joint symmetry. We first construct test functions for each specific property and then investigate the asymptotic properties of their empirical estimators. We demonstrate that the functional boxplot of these sample test functions serves as an informative visualization tool of a given copula structure, effectively measuring the departure from zero of the test function. Furthermore, we introduce a nonparametric testing procedure to assess the significance of deviations from symmetry, ensuring the accuracy and reliability of our visualization method. Through extensive simulation studies involving various copula models, we demonstrate the effectiveness of our testing approach. Finally, we apply our visualization and testing techniques to two real-world datasets: a nutritional habits survey with five variables and wind speed data from three locations in Saudi Arabia.

翻译：Copula结构的可视化和评估对于在多变量数据分析中准确理解和建模相依性至关重要。本文提出了一种创新方法，利用函数箱线图和基于秩的检验程序来评估Copula对称性。该方法专门用于评估反射对称性、径向对称性和联合对称性等关键特征。我们首先为每个特定属性构建检验函数，然后研究其经验估计量的渐近性质。我们证明，这些样本检验函数的函数箱线图可作为给定Copula结构的信息可视化工具，有效衡量检验函数与零值的偏离程度。此外，我们引入了一种非参数检验程序来评估对称性偏离的显著性，确保可视化方法的准确性和可靠性。通过涉及多种Copula模型的广泛模拟研究，我们展示了检验方法的有效性。最后，我们将可视化和检验技术应用于两个真实数据集：一项包含五个变量的营养习惯调查以及沙特阿拉伯三个地点的风速数据。