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Title: Pairwise likelihood estimation for copulas with tractable bivariate margins Authors:  Jan Gorecki - Silesian university in Opava (Czech Republic) [presenting]
Abstract: In moderate to high dimensions, the required probability density function for the standard maximum pseudo-likelihood estimator (MPLE) of a parametric copula is often difficult to obtain, be it analytically in terms of a formula or numerically in terms of a tractable density evaluation procedure. However, the bivariate margins of such copulas are often analytically or numerically tractable. This can be exploited by the introduced pairwise pseudo-likelihood estimator (PPLE), which is studied and compared to the MPLE as an estimator for the parameters of copulas whose densities may not be numerically tractable but whose bivariate margins have tractable densities. Archimedean and related copulas serve as running examples. By simulation, the bias, root mean squared error (RMSE) and run time of the PPLE is studied for Archimedean, hierarchical Archimedean and hierarchical Archimax copulas. The PPLE is also compared to another available estimator suggested for hierarchical Archimedean copulas, the aggregated MPLE (AMPLE). The simulation results indicate that the PPLE has a comparable bias and RMSE with MPLE for those Archimedean copulas where the latter is available. For the hierarchical Archimedean and Archimax copulas where the MPLE is not easily available, the PPLE mostly outperforms the AMPLE in bias and RMSE, moreover with a clear advantage for the PPLE over the AMPLE in terms of run time.