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Extremal index blocks estimator: the threshold and the block size choice
D Prata Gomes1, M Manuela Neves2
1Faculdade de Ciências e Tecnologia and CMA, Universidade Nova de Lisboa, Lisboa, Portugal.
Journal of Applied Statistics
|June 16, 2022
Summary
Estimating the extremal index (θ) is crucial for rare event probability analysis in stationary sequences. This study revisits a block length-dependent estimation procedure, offering a stability criterion for accurate θ estimates.
Area of Science:
- Statistics of Extremes
- Extreme Value Theory
- Time Series Analysis
Background:
- Accurate estimation of the extremal index (θ) is challenging for stationary sequences.
- Existing block estimators for θ require careful selection of threshold and block length.
- Further research is needed to optimize these nuisance parameter choices.
Purpose of the Study:
- To investigate and compare block estimators for the extremal index (θ) in stationary sequences.
- To analyze the impact of threshold and block size on θ estimates.
- To revisit an alternative estimation procedure for θ that relies solely on block length.
Main Methods:
- Utilizing disjoint and sliding block estimators for extremal index estimation.
- Investigating asymptotic properties of block estimators.
- Developing and applying a stability criterion for block length selection in a revised estimation procedure.
Main Results:
- Demonstrated how threshold and block size choices influence extremal index estimates.
- Showcased the stability criterion for selecting block length for a block length-dependent estimator.
- Presented results from extensive simulations and a real-world hydrological data application.
Conclusions:
- The revisited estimation procedure offers a viable alternative for extremal index estimation, contingent on underlying process conditions.
- The proposed stability criterion aids in robust finite-sample estimation of θ.
- The study provides valuable insights for rare event probability analysis in stationary time series.
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