Title: Extreme value estimation for censored regularly varying tails
Authors: Jan Beirlant - KULeuven (Belgium) [presenting]
Abstract: Motivated by applications in long-tail insurance products, we consider tail estimation for right censored data from regularly varying tail models. The bias of the available estimators of the extreme value index can be substantial and depends strongly on the amount of censoring. We review the existing literature, propose a new bias reduced estimator, and show how shrinkage estimation can help to keep the MSE under control. Basic asymptotics results are provided, and a bootstrap algorithm is proposed to construct confidence intervals. We compare these new proposals with the existing estimators through simulation. We also consider the corresponding bivariate problem. Throughout we consider a motor third party liability case from a European country.