Seminars 2007— Abstracts

Friday March 16

Speaker: Peter Schmidt, Michigan State University

Title: Robustness, Redundancy, and Validity of Copulas in Likelihood Models

Abstract: The paper considers likelihood-based estimation of multivariate models, in which only marginal distributions are correctly specified. The unknown joint distribution is modelled with a copula function, which may be misspecified. In a GMM framework, we study robustness and efficiency of resulting estimators, propose improvements to existing estimators and discuss tests of copula validity. It is shown that radially symmetric copulas are robust against misspecification in problems about sample means if the true joint density is also radially symmetric. Efficiency results suggest that knowledge of the true copula is redundant only if the covariance matrix for relevant moment conditions is singular. A simple simulation supports the theoretical result about robustness of the Frank, Farlie-Gumbel-Morgenstern and Ali-Mikhail-Haq copula families.

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