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Inference for the limiting cluster size distribution of extreme values. (English) Zbl 1158.62061

Summary: Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily a compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The underlying Poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes.
We introduce estimators of the limiting cluster size probabilities, which are constructed through a recursive algorithm. We derive estimators of the extremal index which plays a key role in determining the intensity of cluster positions. We study the asymptotic properties of the estimators and investigate their finite sample behavior on simulated data.

MSC:

62M99 Inference from stochastic processes
60G70 Extreme value theory; extremal stochastic processes
62G32 Statistics of extreme values; tail inference
62E20 Asymptotic distribution theory in statistics
62M09 Non-Markovian processes: estimation
62G20 Asymptotic properties of nonparametric inference
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