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Title: Two-step robust estimation of copulae Authors:  Samuel Orso - University of Geneva (Switzerland) [presenting]
Stephane Guerrier - University of Illinois at Urbana-Champaign (United States)
Maria-Pia Victoria-Feser - University of Geneva (Switzerland)
Abstract: Copula is a flexible tool for modeling multivariate random variables. Inference is generally based on multi-step estimators to preserve this flexibility. We address the problem of robustness in this context. It is challenging for many reasons: (a) How to built a gross error model that encompasses issues arising in multiple dimensions? (b) How to built multi-step robust estimators with good asymptotic properties? (c) How to obtain computationally feasible estimators and their inference? We concentrate our efforts in the two-dimensional case. First, we propose a new gross error model from which the influence function is derived for two-step M-estimators. Second, we prove the strong consistency and asymptotic normality under weak conditions. Third, we propose a fast bootstrap procedure to obtain the covariance matrix of the two-step estimators. We illustrate the estimating procedure with a new R package under development.