A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.

中文翻译：

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连续变量的秩不变等级聚类的不相似函数

为连续随机向量之间的相似性（基于copula）的概念提供了理论框架，并研究了其主要性质。拟议的相异性将最小值分配给一对单调的随机向量。研究了这种相异性的各种属性，并特别注意那些易于使用分层凝聚方法的属性，例如可还原性。提供了一些在聚类算法中使用这种度量的见解，并提供了仿真研究。实际案例研究说明了整个方法的主要特征。