Robust Learning of Tail Dependence

Accurate estimation of tail dependence is difficult due to model misspecification and data contamination. This paper introduces a class of minimum f-divergence estimators for the tail dependence coefficient that unifies robust estimation with extreme value theory. I establish strong consistency and derive the semiparametric efficiency bound for estimating extremal dependence, the extremal Cramér–Rao bound. I show that the estimator achieves this bound if and only if the second derivative of its generating function at unity equals one, formally characterizing the trade-off between robustness and asymptotic efficiency. An empirical application to systemic risk in the US banking sector shows that the robust Hellinger estimator provides stability during crises, while the efficient maximum likelihood estimator offers precision during normal periods.