WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 23, 2024
New Approaches to Extremal Index Estimation
Authors: , ,
Abstract: The extremal index is a parameter associated with the extreme value distributions of dependent
stationary sequences. Under certain local dependence conditions, exceedances above a specified threshold tend
to occur in isolated clusters. The reciprocal of the extremal index can be interpreted as the limiting size of these
clusters. Accurately estimating the size of such clusters is crucial for analyzing real data and can significantly
influence decision making processes that impact population well being. The paper presents a recent method for
the estimation of the extremal index which starts by the estimation of the parameter itself and, only then, to use
that estimate in the cluster mean size estimation. The procedure starts with the estimation of a specific proportion
by the corresponding relative frequency. Thus, it is very simple, intuitive, it has good statistical properties, and it
does not depend on the method used for the mean cluster estimation. The interpretation of the extremal index as
a proportion is known, but it has not been used directly as an estimation method. In recent years, various authors
have proposed different estimators for the extremal index. This paper applies some of the latest estimation methods
for the extremal index to real data and analyses their performance using training and test samples. The results
are compared with other well known estimators, for which R packages are available. The results show a better
performance of the Proportion estimator, followed by the Gaps estimator, when compared to the other considered
index estimators.
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Keywords: Extremal Value Theory, Extremal index, Robust estimation, Proportion estimator, Negative
Binomial, Stationary sequences, Clusters of exceedances
Pages: 223-231
DOI: 10.37394/23202.2024.23.25