Markovich, Natalia and Rodionov, Igor (2023) Threshold selection for extremal index estimation. Journal of Nonparametric Statistics, 36 (3). pp. 527-546. DOI https://doi.org/10.1080/10485252.2023.2266050
Markovich, Natalia and Rodionov, Igor (2023) Threshold selection for extremal index estimation. Journal of Nonparametric Statistics, 36 (3). pp. 527-546. DOI https://doi.org/10.1080/10485252.2023.2266050
Markovich, Natalia and Rodionov, Igor (2023) Threshold selection for extremal index estimation. Journal of Nonparametric Statistics, 36 (3). pp. 527-546. DOI https://doi.org/10.1080/10485252.2023.2266050
Abstract
We propose a new threshold selection method for nonparametric estimation of the extremal index of stochastic processes. The 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. A modification of the discrepancy statistic based on the Cramér-von Mises-Smirnov statistic ω² is calculated by k largest order statistics instead of an entire sample. Its asymptotic distribution as k → ∞ is proved to coincide with the ω²-distribution. Its quantiles are used as discrepancy values. The convergence rate 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. It may be applied to other estimators of the extremal index. The performance of our method is evaluated by simulated and real data examples
Item Type: | Article |
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Uncontrolled Keywords: | Cramér-von Mises-Smirnov statistic; Discrepancy method; Extremal index; Nonparametric estimation; Threshold selection |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 20 Sep 2023 16:56 |
Last Modified: | 13 Oct 2024 01:00 |
URI: | http://repository.essex.ac.uk/id/eprint/36226 |
Available files
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