Jan Beirlant & Chen Zhou


At Delft University of Technology

Jan Beirlant (Catholic University of Leuven)

Title: Bias reduced estimation of the extreme value index

Abstract: A lot of attention has been paid to bias reduced estimation of the extreme value index in case of heavy-tailed distributions. In this talk we present some proposals for all max-domains of attraction. A first method is based on ridge regression for generalized quantiles. Secondly we discuss the use of Bernstein polynomials for estimating the bias in the Peaks over Threshold method.

Chen Zhou (De Nederlandsche Bank and Erasmus University of Rotterdam)

Title: Trends in extreme value indices

Abstract: We consider extreme value analysis for independent but non-identically distributed observations. In particular, the observations do not share the same extreme value index. This situation is related to, but differs from, heteroscedastic extremes in Einmahl et al. (2016). Compared to the heteroscedastic extremes, our model allows for a broader class in which tails of the probability distributions of different observations are of different order. In other words, we are dealing with distributions that differ much more than the heteroscedastic extremes. Assuming continuously changing extreme value indices, we provide a non-parametric estimate for the functional extreme value index. Besides estimating the extreme value index locally, we also provide a global estimator for the trend and its joint asymptotic property. The global asymptotic property can be used for testing a pre-specified parametric trend in the extreme value indices. In particular, it can be applied to test whether the extreme value index remains at a constant level across all observations.