Compound Poisson approximation for simple transient random walks in random sceneries

Chenavier, Nicolas; Darwiche, Ahmad; Rousselle, Arnaud

doi:10.30757/alea.v21-12

ALEA

2024

DOI: 10.30757/alea.v21-12

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Compound Poisson approximation for simple transient random walks in random sceneries

Nicolas Chenavier,

Ahmad Darwiche,

Arnaud Rousselle

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2024

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Cited by 1 publication

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New Approaches to Extremal Index Estimation

Miranda,

De Miranda,

Gomes

2024

Wseas Transactions on Systems

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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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New Approaches to Extremal Index Estimation

Miranda,

De Miranda,

Gomes

2024

Wseas Transactions on Systems

View full text Add to dashboard Cite

show abstract

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Compound Poisson approximation for simple transient random walks in random sceneries

Cited by 1 publication

References 18 publications

New Approaches to Extremal Index Estimation

New Approaches to Extremal Index Estimation

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