At Tilburg University

## Xuan Leng (Erasmus University Rotterdam)

**Title**: Bias correction for the maximum likelihood estimator of the extreme value index

**Abstract**: This paper conducts bias correction for the maximum likelihood estimator (MLE) of the extreme value index. Compared to the original MLE, the bias corrected estimator allows for using a larger fraction of observations in tail region for estimation, which results in a lower asymptotic variance. The bias correction is achieved by subtracting the asymptotic bias from the original MLE, which is estimated by a two-step approach. We prove the asymptotic behavior of the proposed bias-corrected estimator. Extensive simulations show the superiority of the bias-corrected estimator compared to existing estimators of the extreme value index. We apply the bias-corrected MLE to test whether human life span is unlimited.

## Philippe Naveau (CNRS-France)

**Title**: Analysis of extreme climate events by combining multivariate extreme values theory and causality theory

**Abstract**: The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for the extremal index, essentially due to Northrop (2015) [An efficient semiparametric maxima estimator of the extremal index. Extremes 18, 585–603], are analyzed in detail. In contrast to many competitors, the estimators only depend on the choice of one parameter sequence. We derive an asymptotic expansion, prove asymptotic normality and show consistency of an estimator for the asymptotic variance. Explicit calculations in certain models and a finite-sample Monte Carlo simulation study reveal that the sliding blocks estimator outperforms other blocks estimators, and that it is competitive to runs- and inter-exceedance estimators in various models. The methods are applied to a variety of financial time series.