Flexible pair-copula estimation in D-vines using bivariate penalized splines |
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Authors: | Göran Kauermann Christian Schellhase |
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Affiliation: | 1. Department of Statistics, Ludwig-Maximilians-University Munich, Ludwigstra?e 33, 80539, Munich, Germany 2. Department for Business Administration and Economics, Bielefeld University, Postfach 10 01 31, 33501, Bielefeld, Germany
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Abstract: | The paper presents a new method for flexible fitting of D-vines. Pair-copulas are estimated semi-parametrically using penalized Bernstein polynomials or constant and linear B-splines, respectively, as spline bases in each knot of the D-vine throughout each level. A penalty induce smoothness of the fit while the high dimensional spline basis guarantees flexibility. To ensure uniform univariate margins of each pair-copula, linear constraints are placed on the spline coefficients and quadratic programming is used to fit the model. The amount of penalizations for each pair-copula is driven by a penalty parameter which is selected in a numerically efficient way. Simulations and practical examples accompany the presentation. |
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