A sliding blocks estimator for the extremal index

Robert, Christian Y.;Segers, Johan;Ferro, Christopher A.T.
(2009) Electronic Journal of Statistics — Vol. 3, p. 993-1020 (2009)

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Authors
  • Robert, Christian Y.Ecole Nationale de la Statistique et de l'Administration Economique
    Author
  • Segers, JohanUCLouvain
    Author
  • Ferro, Christopher A.T.University of Exeter
    Author
Abstract
In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper we focus on the estimation of the extremal index which measures the degree of clustering of extremes. We consider disjoint and sliding blocks estimators and compare their asymptotic properties. In particular we show that the sliding blocks estimator is more efficient than the disjoint version and has a smaller asymptotic bias. Moreover we propose a method to reduce its bias when considering sufficiently large block sizes.
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Robert, C. Y., Segers, J., & Ferro, C. A. T. (2009). A sliding blocks estimator for the extremal index. Electronic Journal of Statistics, 3, 993-1020. https://doi.org/10.1214/08-EJS345 (Original work published 2009)