A Decomposition of Copulas and Its Use |
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| Authors: | Engin A Sungur Peh Ng |
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| Institution: | 1. Division of Science and Mathematics , University of Minnesota, Morris , Morris, Minnesota, USA sungurea@morris.umn.edu;3. Division of Science and Mathematics , University of Minnesota, Morris , Morris, Minnesota, USA |
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| Abstract: | ABSTRACT In this article, we create a decomposition that represents and describes the depen-dence structure between two variables. Since copulas provide a deep understanding of the dependence structure by eliminating the effects of the marginals, they play a key role in this study. We define a discretized copula density matrix and decompose it into a set of permutation matrices by using the Birkhoff–von Neumann theorem. This decomposition provides a way to effectively apply the concepts of copulas to solve problems in multivariate statistical data analysis. |
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| Keywords: | Birkhoff–von Neumann theorem Copulas Discretized copulas Doubly stochastic matrix Gini's measure Permutation matrix Prior probability |
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