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A sliding blocks estimator for the extremal index. (English) Zbl 1326.60075

Summary: 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.

MSC:

60G70 Extreme value theory; extremal stochastic processes
62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference
62G32 Statistics of extreme values; tail inference
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