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Estimating Archimedean Copulas in High Dimensions


Christian Hering, Institute of Number Theory and Probability Theory, University of Ulm, 89069 Ulm, Germany.


Abstract.  This article presents a novel estimation procedure for high-dimensional Archimedean copulas. In contrast to maximum likelihood estimation, the method presented here does not require derivatives of the Archimedean generator. This is computationally advantageous for high-dimensional Archimedean copulas in which higher-order derivatives are needed but are often difficult to obtain. Our procedure is based on a parameter-dependent transformation of the underlying random variables to a one-dimensional distribution where a minimum-distance method is applied. We show strong consistency of the resulting minimum-distance estimators to the case of known margins as well as to the case of unknown margins when pseudo-observations are used. Moreover, we conduct a simulation comparing the performance of the proposed estimation procedure with the well-known maximum likelihood approach according to bias and standard deviation.