Estimation techniques and goodness-of-fit tests for certain copula classes in large dimensions
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
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Whenever multivariate data has to be modelled, a copula approach naturally comes into play. As a distribution function on the multivariate unit cube with standard uniform margins a copula may be used to characterize the dependence structure of a random vector. This dissertation deals with three particular classes of copulas. These are the classes of exchangeable Archimedean, nested Archimedean and extensible Marshall-Olkin copulas. Goodness-of-fit tests and parameter estimation techniques for exchangeable Archimedean copulas are presented. These are based on an easy transformation originally used for sampling purposes and are hence tailor-made for large dimensional problems often encountered in practice. Strong consistency of the suggested estimators is proven and large-scale simulation studies investigate their finite sample behaviour. Moreover, a two step parameter estimation procedure for nested Archimedean copulas is suggested and weak consistency is proven under relatively mild conditions. As before, a simulation study is conducted to compare the suggested estimator to other, well-known approaches. In addition, a new probabilistic model for nested Archimedean copulas is given and used for sampling purposes. Finally, an estimation approach for extensible Marshall-Olkin copulas is presented. The strategy of the suggested approach is to match an empirical quantity with its theoretical counterpart. Therefore, no density of the underlying copula is needed having the advantage that the estimation procedure may be applied in arbitrary dimensions. In fact, the resulting estimator even improves if the dimension becomes larger.
Subject HeadingsKopula <Mathematik> [GND]
Goodness-of-fit tests [LCSH]
Parameter estimation [LCSH]