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Asymptotic expansions for blocks estimators: PoT framework

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  • Chen, Zaoli
  • Kulik, Rafał

Abstract

We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a complete description of the limiting behaviour of these estimators. This is achieved by a precise expansion for the difference between the sliding and the disjoint blocks statistics. The rates in the expansion stem from internal clusters and boundary clusters. To obtain these rates we need to extend the existing results on vague convergence of cluster measures. We reveal dichotomous behaviour between small blocks and large blocks scenario.

Suggested Citation

  • Chen, Zaoli & Kulik, Rafał, 2026. "Asymptotic expansions for blocks estimators: PoT framework," Stochastic Processes and their Applications, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:spapps:v:191:y:2026:i:c:s0304414925001875
    DOI: 10.1016/j.spa.2025.104744
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    References listed on IDEAS

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