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24 April 2024 |
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Threshold selection for extremal index estimation | | Natalia M. Markovich
; Igor V. Rodionov
; | | Date: |
4 Sep 2020 | | Abstract: | We propose a new threshold selection method for the nonparametric estimation
of the extremal index of stochastic processes. The so-called discrepancy method
was proposed as a data-driven smoothing tool for estimation of a probability
density function. Now it is modified to select a threshold parameter of an
extremal index estimator. To this end, a specific normalization of the
discrepancy statistic based on the Cramér-von Mises-Smirnov statistic
$omega^2$ is calculated by the $k$ largest order statistics instead of an
entire sample. Its asymptotic distribution as $k oinfty$ is proved to be the
same as the $omega^2$-distribution. The quantiles of the latter distribution
are used as discrepancy values. The rate of convergence of an extremal index
estimate coupled with the discrepancy method is derived. The discrepancy method
is used as an automatic threshold selection for the intervals and $K-$gaps
estimators and it may be applied to other estimators of the extremal index. | | Source: | arXiv, 2009.02318 | | Services: | Forum | Review | PDF | Favorites | |
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