Extremal index: estimation and resampling

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.

Automated summary

This study considers the cycles estimator introduced in Ferreira and Ferreira (Ann Inst Henri Poincare Probab Stat 54(2):587-605, 2018) within Extreme Value Theory. A reduced bias estimator based on the Jackknife methodology is presented, along with the application of the bootstrap technique for inference and obtaining confidence intervals. Performance analysis based on simulation indicates that our proposal effectively reduces bias and compares favorably with some well-known methods. Additionally, the methods are applied to real data.