Memorandum 1809

Modeling dependence

W.C.M. Kallenberg

Abstract:
A new way of choosing a suitable copula to model dependence is introduced. Instead of relying on a given parametric family of copulas or applying the other extreme of modeling dependence in a nonparametric way, an intermediate approach is proposed, based on a sequence of parametric models containing more and more dependency aspects. In contrast to a similar way of thinking in testing theory, the method here, intended for estimating the copula, often requires a somewhat larger number of steps. One approach is based on exponential families, another on contamination families. An extensive numerical investigation is supplied on a large number of well known copulas. The method based on contamination families is recommended. A Gaussian start in this approximation looks very promising.

Keywords:   Copula, Legendre polynomials, exponential family, contamination family, nonlinear correlation

Mathematics Subject Classification:   62H12, 62H20, 62P05

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