Excess Mean of Power Estimator of Extreme Value Index

Ngai Hang Chan; Yuxin Li; Tony Sit

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

Excess Mean of Power Estimator of Extreme Value Index

Ngai Hang Chan^*, Yuxin Li, Tony Sit

^*Corresponding author for this work

Department of Biostatistics

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 12 - Chapter in an edited book (Author) › peer-review

1 Citation (Scopus)

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. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023

Original language	English
Title of host publication	Research Papers in Statistical Inference for Time Series and Related Models
Subtitle of host publication	Essays in Honor of Masanobu Taniguchi
Editors	Yan Liu, Junichi Hirukawa, Yoshihide Kakizawa
Place of Publication	Singapore
Publisher	Springer
Chapter	2
Pages	25-82
Number of pages	58
ISBN (Electronic)	978-981-99-0803-5
ISBN (Print)	978-981-99-0802-8, 978-981-99-0805-9
DOIs	https://doi.org/10.1007/978-981-99-0803-5_2
Publication status	Published - 23 Jul 2023

Funding

The authors would like to thank the Editors for their kind invitation to contribute to this important treatise in honor of Professor Taniguchi, and in particular, to an anonymous referee for meticulous and critical readings and suggestions, which improve this manuscript tremendously. Research supported in part by grants from the Research Grants Council of Hong Kong, HKSAR-RGC-GRF Nos 14308218 and 14307921 (NH Chan), and Nos 14301618, 14301920, and 14307221 (T Sit).

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GRF: Statistical Modeling of Big Data Networks
CHAN, N. H. (Principal Investigator / Project Coordinator) & CHEUNG, K. C. (Co-Investigator)
1/01/22 → …
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title = "Excess Mean of Power Estimator of Extreme Value Index",

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. {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023",

author = "Chan, {Ngai Hang} and Yuxin Li and Tony Sit",

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Excess Mean of Power Estimator of Extreme Value Index. / Chan, Ngai Hang; Li, Yuxin; Sit, Tony.
Research Papers in Statistical Inference for Time Series and Related Models: Essays in Honor of Masanobu Taniguchi. ed. / Yan Liu; Junichi Hirukawa; Yoshihide Kakizawa. Singapore: Springer , 2023. p. 25-82.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 12 - Chapter in an edited book (Author) › peer-review

TY - CHAP

T1 - Excess Mean of Power Estimator of Extreme Value Index

AU - Chan, Ngai Hang

AU - Li, Yuxin

AU - Sit, Tony

PY - 2023/7/23

Y1 - 2023/7/23

N2 - 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. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023

AB - 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. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023

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DO - 10.1007/978-981-99-0803-5_2

M3 - RGC 12 - Chapter in an edited book (Author)

SN - 978-981-99-0802-8

SN - 978-981-99-0805-9

SP - 25

EP - 82

BT - Research Papers in Statistical Inference for Time Series and Related Models

A2 - Liu, Yan

A2 - Hirukawa, Junichi

A2 - Kakizawa, Yoshihide

PB - Springer

CY - Singapore

ER -

Excess Mean of Power Estimator of Extreme Value Index

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