# Weak convergence of a pseudo maximum likelihood estimator for the extremal index

@article{Berghaus2016WeakCO, title={Weak convergence of a pseudo maximum likelihood estimator for the extremal index}, author={Betina Berghaus and Axel Bucher}, journal={arXiv: Statistics Theory}, year={2016} }

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 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… Expand

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