Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments

Frederico Caeiro; M. Ivette Gomes

doi:10.1007/978-3-031-12766-3_3

Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments

Frederico Caeiro, M. Ivette Gomes

CMA - Centro de Matemática e Aplicações

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Citations (Scopus)

Abstract

In statistics of extremes, the estimation of the extreme value index (EVI) is an important and central topic of research. We consider the probability weighted moment estimator of the EVI, based on the largest observations. Due to the specificity of the properties of the estimator, a direct estimation of the threshold is not straightforward. In this work, we consider an adaptive choice of the number of order statistics based on the double bootstrap methodology. Computational and empirical properties of the methodology are here provided.

Original language	English
Title of host publication	Recent Developments in Statistics and Data Science
Subtitle of host publication	SPE2021, Évora, Portugal, October 13–16
Editors	Regina Bispo, Lígia Henriques-Rodrigues, Russell Alpizar-Jara, Miguel de Carvalho
Place of Publication	Cham
Publisher	Springer
Pages	29-39
Number of pages	11
ISBN (Electronic)	978-3-031-12766-3
ISBN (Print)	978-3-031-12765-6
DOIs	https://doi.org/10.1007/978-3-031-12766-3_3
Publication status	Published - 29 Nov 2022
Event	25th Congress of the Portuguese Statistical Society, SPE 2021 - Virtual, Online Duration: 13 Oct 2021 → 16 Oct 2021

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Publisher	Springer
Volume	398
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	25th Congress of the Portuguese Statistical Society, SPE 2021
City	Virtual, Online
Period	13/10/21 → 16/10/21

Keywords

Bootstrap
Extreme value index
Heavy tails
Probability weighted moment
Semi-parametric estimation

Access to Document

10.1007/978-3-031-12766-3_3

Cite this

Caeiro, F., & Gomes, M. I. (2022). Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments. In R. Bispo, L. Henriques-Rodrigues, R. Alpizar-Jara, & M. de Carvalho (Eds.), Recent Developments in Statistics and Data Science: SPE2021, Évora, Portugal, October 13–16 (pp. 29-39). (Springer Proceedings in Mathematics and Statistics; Vol. 398). Springer. https://doi.org/10.1007/978-3-031-12766-3_3

Caeiro, Frederico ; Gomes, M. Ivette. / Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments. Recent Developments in Statistics and Data Science: SPE2021, Évora, Portugal, October 13–16. editor / Regina Bispo ; Lígia Henriques-Rodrigues ; Russell Alpizar-Jara ; Miguel de Carvalho. Cham : Springer, 2022. pp. 29-39 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{66e5b29819b8430eab9523501da5ccfc,

title = "Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments",

abstract = "In statistics of extremes, the estimation of the extreme value index (EVI) is an important and central topic of research. We consider the probability weighted moment estimator of the EVI, based on the largest observations. Due to the specificity of the properties of the estimator, a direct estimation of the threshold is not straightforward. In this work, we consider an adaptive choice of the number of order statistics based on the double bootstrap methodology. Computational and empirical properties of the methodology are here provided.",

keywords = "Bootstrap, Extreme value index, Heavy tails, Probability weighted moment, Semi-parametric estimation",

author = "Frederico Caeiro and Gomes, {M. Ivette}",

note = "Funding Information: Acknowledgements Research partially supported by National Funds through FCT—Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia, projects UIDB/00006/2020 and UIDP/00006/2020 (CEA/UL) and UIDB/00297/2020 and UIDP/00297/2020 (CMA/UNL). Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 25th Congress of the Portuguese Statistical Society, SPE 2021 ; Conference date: 13-10-2021 Through 16-10-2021",

year = "2022",

month = nov,

day = "29",

doi = "10.1007/978-3-031-12766-3_3",

language = "English",

isbn = "978-3-031-12765-6",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "29--39",

editor = "Regina Bispo and L{\'i}gia Henriques-Rodrigues and Russell Alpizar-Jara and {de Carvalho}, Miguel",

booktitle = "Recent Developments in Statistics and Data Science",

address = "Netherlands",

}

Caeiro, F & Gomes, MI 2022, Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments. in R Bispo, L Henriques-Rodrigues, R Alpizar-Jara & M de Carvalho (eds), Recent Developments in Statistics and Data Science: SPE2021, Évora, Portugal, October 13–16. Springer Proceedings in Mathematics and Statistics, vol. 398, Springer, Cham, pp. 29-39, 25th Congress of the Portuguese Statistical Society, SPE 2021, Virtual, Online, 13/10/21. https://doi.org/10.1007/978-3-031-12766-3_3

Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments. / Caeiro, Frederico; Gomes, M. Ivette.
Recent Developments in Statistics and Data Science: SPE2021, Évora, Portugal, October 13–16. ed. / Regina Bispo; Lígia Henriques-Rodrigues; Russell Alpizar-Jara; Miguel de Carvalho. Cham: Springer, 2022. p. 29-39 (Springer Proceedings in Mathematics and Statistics; Vol. 398).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments

AU - Caeiro, Frederico

AU - Gomes, M. Ivette

N1 - Funding Information: Acknowledgements Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, projects UIDB/00006/2020 and UIDP/00006/2020 (CEA/UL) and UIDB/00297/2020 and UIDP/00297/2020 (CMA/UNL). Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022/11/29

Y1 - 2022/11/29

N2 - In statistics of extremes, the estimation of the extreme value index (EVI) is an important and central topic of research. We consider the probability weighted moment estimator of the EVI, based on the largest observations. Due to the specificity of the properties of the estimator, a direct estimation of the threshold is not straightforward. In this work, we consider an adaptive choice of the number of order statistics based on the double bootstrap methodology. Computational and empirical properties of the methodology are here provided.

AB - In statistics of extremes, the estimation of the extreme value index (EVI) is an important and central topic of research. We consider the probability weighted moment estimator of the EVI, based on the largest observations. Due to the specificity of the properties of the estimator, a direct estimation of the threshold is not straightforward. In this work, we consider an adaptive choice of the number of order statistics based on the double bootstrap methodology. Computational and empirical properties of the methodology are here provided.

KW - Bootstrap

KW - Extreme value index

KW - Heavy tails

KW - Probability weighted moment

KW - Semi-parametric estimation

UR - http://www.scopus.com/inward/record.url?scp=85144348871&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-12766-3_3

DO - 10.1007/978-3-031-12766-3_3

M3 - Conference contribution

AN - SCOPUS:85144348871

SN - 978-3-031-12765-6

T3 - Springer Proceedings in Mathematics and Statistics

SP - 29

EP - 39

BT - Recent Developments in Statistics and Data Science

A2 - Bispo, Regina

A2 - Henriques-Rodrigues, Lígia

A2 - Alpizar-Jara, Russell

A2 - de Carvalho, Miguel

PB - Springer

CY - Cham

T2 - 25th Congress of the Portuguese Statistical Society, SPE 2021

Y2 - 13 October 2021 through 16 October 2021

ER -

Caeiro F, Gomes MI. Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments. In Bispo R, Henriques-Rodrigues L, Alpizar-Jara R, de Carvalho M, editors, Recent Developments in Statistics and Data Science: SPE2021, Évora, Portugal, October 13–16. Cham: Springer. 2022. p. 29-39. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-031-12766-3_3

Computational Study of the Adaptive Estimation of the Extreme Value Index with Probability Weighted Moments

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this