A nonparametric estimator of the extremal index

Dr. J.-J. Cai

Assistant Professor in Statistics

Delft Institute of Applied Mathematics

Delft University of Technology

Research interests:

Statistics of Extremes

Asymptotic Statistics

Non-Parametric Statistics

Probabilistic forecast of extreme events

Clustering of extremes has a large societal impact. The extremal index, a number in the unit interval, is a key parameter in modelling the clustering of extremes. We build a connection between the extremal index and the stable tail dependence function, which enables us to compute the value of extremal indices for some time series models. We also construct a nonparametric estimator of the extremal index and an estimation procedure to verify D^(d)(u_n) condition, a local dependence condition often assumed when studying extremal index. We prove that the estimators are asymptotically normal. The simulation study compares our estimator to two existing methods, which shows that our method has good finite sample properties. We apply our method to estimate the expected durations of heatwaves in the Netherlands and in Greece.