Comparison on estimations for the extremal index
Vergelijken van schatters van de extreme index
J.A.M.L. Clercx (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Juanjuan Cai – Mentor (TU Delft - Statistics)
LE Meester – Graduation committee member (TU Delft - Applied Probability)
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Abstract
The clustering of events can have a large impact on society. The extremal index $\theta$ tells how much extreme events cluster. We will compare different types of estimators in this project. First, we review the extremes of different sequences which have different values of $\theta$. We have found significant differences between the extremes. Then, 2 different types of estimators are introduced which both use different ways to divide the data, using disjoint blocks and using sliding blocks. The optimal block lengths are simulated for all those estimators. Using those block lengths, $\theta$ is simulated with all the estimators. From the simulations we conclude that the estimators using sliding blocks perform better. The best-performed estimator that we found from the simulations is used to estimate $\theta$ on data from the KNMI, comparing wind gusts and precipitation at weather stations De Bilt and Vlissingen.