A closed-form universal trivariate pair-copula
نویسنده
چکیده
Based on the trivariate pair-copula construction for the bivariate linear circular copula by Perlman and Wellner (Symmetry 3:574-99, 2011) and the Theorem of Carathéodory, which states that any valid correlation matrix is a finite convex combination of extreme correlation matrices, we generate a class of closed-form analytical 3-universal copulas. We derive explicit product and lifting copula formulas for the set of all extremal correlation matrices. Our analytical proof makes use of a novel set of conditional copula inequalities, which are of independent interest.
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