Asymptotic distributions for the intervals estimators of the extremal index and the cluster-size probabilities |
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Authors: | C.Y. Robert |
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Affiliation: | Ecole Nationale de la Statistique et de l’Administration Economique, Timbre J120, 3 Avenue Pierre Larousse, 92245 Malakoff Cedex, France |
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Abstract: | Under appropriate long range dependence conditions, the point process of exceedances of a stationary sequence weakly converges to a homogeneous compound Poisson point process. This limiting point process can be characterized by the extremal index and the cluster-size probabilities. In this paper we address the problem of estimating these quantities and we consider the intervals estimators introduced in Ferro and Segers [2003. Inference for clusters of extreme values. J. Roy. Statist. Soc. Ser. B 545–556] and in Ferro [2004. Statistical methods for clusters of extreme values. Ph.D. Thesis, Lancaster University]. We establish asymptotic weak convergence to Gaussian random variables and we give their asymptotic variance. |
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Keywords: | Extreme value statistics Extremal index Cluster-size distribution Intervals estimators Point process of exceedances |
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