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On the asymptotics of extremal lp-blocks cluster inference

Gloria Buritic\'a (UNIGE)Olivier Wintenberger (LPSM (UMR\_8001))
Dec 2022
摘要
Extremes occur in stationary regularly varying time series as short periodswith several large observations, known as extremal blocks. We study clusterstatistics summarizing the behavior of functions acting on these extremalblocks. Examples of cluster statistics are the extremal index, cluster sizeprobabilities, and other cluster indices. The purpose of our work is twofold.First, we state the asymptotic normality of block estimators for clusterinference based on consecutive observations with large lp-norms, for p > 0.Second, we verify the conditions we require on classic models such as linearmodels and solutions of stochastic recurrence equations. Regarding linearmodels, we prove that the asymptotic variance of classical index cluster-basedestimators is null as first conjectured in Hsing T. [26]. We illustrate ourfindings on simulations.
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