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2020 | OriginalPaper | Chapter

The Discrepancy Method for Extremal Index Estimation

Author : Natalia Markovich

Published in: Nonparametric Statistics

Publisher: Springer International Publishing

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Abstract

We consider the nonparametric estimation of the extremal index of stochastic processes. The discrepancy method that was proposed by the author as a data-driven smoothing tool for probability density function estimation is extended to find a threshold parameter u for an extremal index estimator in case of heavy-tailed distributions. To this end, the discrepancy statistics are based on the von Mises–Smirnov statistic and the k largest order statistics instead of an entire sample. The asymptotic chi-squared distribution of the discrepancy measure is derived. Its quantiles may be used as discrepancy values. An algorithm to select u for an estimator of the extremal index is proposed. The accuracy of the discrepancy method is checked by a simulation study.

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previous chapter Semiparametric Weighting Estimations of a Zero-Inflated Poisson Regression with Missing in Covariates
next chapter Correction for Optimisation Bias in Structured Sparse High-Dimensional Variable Selection
Footnotes
1
\(L=1\) holds when \(\theta =0\).
 
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Metadata
Title
The Discrepancy Method for Extremal Index Estimation
Author
Natalia Markovich
Copyright Year
2020
Book
Nonparametric Statistics

Print ISBN: 978-3-030-57305-8

Electronic ISBN: 978-3-030-57306-5

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-57306-5_31

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