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Extremal index: estimation and resampling

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  • Marta Ferreira

    (Universidade do Minho)

Abstract

The duration of extremes in time leads to a phenomenon known as clustering of high values, with a strong impact on risk assessment. The extremal index is a measure developed within Extreme Value Theory that quantifies the degree of clustering of high values. In this work we will consider the cycles estimator introduced in Ferreira and Ferreira (Ann Inst Henri Poincare Probab Stat 54(2):587–605, 2018). A reduced bias estimator based on the Jackknife methodology will be presented. The bootstrap technique will also be considered in the inference and will allow to obtain confidence intervals. The performance will be analyzed based on simulation. We found our proposal effective in reducing bias and it compares favorably with some well-known methods. An application of the methods to real data will also be presented.

Suggested Citation

  • Marta Ferreira, 2024. "Extremal index: estimation and resampling," Computational Statistics, Springer, vol. 39(5), pages 2703-2720, July.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:5:d:10.1007_s00180-023-01406-9
    DOI: 10.1007/s00180-023-01406-9
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    References listed on IDEAS

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    1. J. Sebastião & A. Martins & H. Ferreira & L. Pereira, 2013. "Estimating the upcrossings index," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 549-579, November.
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    5. Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
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    8. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556, May.
    9. Gomes, M. Ivette & Hall, Andreia & Miranda, M. Cristina, 2008. "Subsampling techniques and the Jackknife methodology in the estimation of the extremal index," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2022-2041, January.
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