Excess Mean of Power Estimator of Extreme Value Index

Ngai Hang Chan (), Yuxin Li () and Tony Sit ()
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Ngai Hang Chan: City University of Hong Kong
Yuxin Li: The Chinese University of Hong Kong
Tony Sit: The Chinese University of Hong Kong

Chapter Chapter 2 in Research Papers in Statistical Inference for Time Series and Related Models, 2023, pp 25-82 from Springer

Abstract: Abstract We propose a new type of extreme value index (EVI) estimator, namely, excess mean of power (EMP) estimator, which can be regarded as an average of the existing mean of order p (MOP) estimators over different thresholds. The asymptotic normalities of the MOP and EMP estimators for dependent observations are established under some mild conditions. We also develop consistent estimators for the asymptotic variances of the MOP and EMP estimators. Furthermore, the asymptotic normality of the extreme quantile estimator is established for dependent observations from which confidence intervals for the extreme quantile can be constructed. The proposed EMP estimator not only attains the best efficiency among typical EVI estimators under the optimal threshold, but is also more robust with respect to the choice of threshold.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-0803-5_2

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DOI: 10.1007/978-981-99-0803-5_2

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