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A high quantile estimator based on the log-generalized Weibull tail limit. / de Valk, Cees; Cai, Juan-Juan.

In: Econometrics and Statistics, Vol. 6, 2018, p. 107-128.

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de Valk, Cees ; Cai, Juan-Juan. / A high quantile estimator based on the log-generalized Weibull tail limit. In: Econometrics and Statistics. 2018 ; Vol. 6. pp. 107-128.

BibTeX

@article{2cf52fdd24084e38b3dddadf553a6a9b,
title = "A high quantile estimator based on the log-generalized Weibull tail limit",
abstract = "The estimation of high quantiles for very low probabilities of exceedance pn much smaller than 1/n (with n the sample size) remains a major challenge. For this purpose, the log-Generalized Weibull (log-GW) tail limit was recently proposed as regularity condition as an alternative to the Generalized Pareto (GP) tail limit, in order to avoid potentially severe bias in applications of the latter. Continuing in this direction, a new estimator for the log-GW tail index and a related quantile estimator are introduced. Both are constructed using the Hill estimator as building block. Sufficient conditions for asymptotic normality are established. These results, together with the results of simulations and an application, indicate that the new estimator fulfils the potential of the log-GW tail limit as a widely applicable model for high quantile estimation, showing a substantial reduction in bias as well as improved precision when compared to an estimator based on the GP tail limit.",
keywords = "High quantile, Hill estimator, Log-generalized Weibull tail limit, Log-GW tail index",
author = "{de Valk}, Cees and Juan-Juan Cai",
year = "2018",
doi = "10.1016/j.ecosta.2017.03.001",
language = "English",
volume = "6",
pages = "107--128",
journal = "Econometrics and Statistics",
issn = "2468-0389",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - A high quantile estimator based on the log-generalized Weibull tail limit

AU - de Valk, Cees

AU - Cai, Juan-Juan

PY - 2018

Y1 - 2018

N2 - The estimation of high quantiles for very low probabilities of exceedance pn much smaller than 1/n (with n the sample size) remains a major challenge. For this purpose, the log-Generalized Weibull (log-GW) tail limit was recently proposed as regularity condition as an alternative to the Generalized Pareto (GP) tail limit, in order to avoid potentially severe bias in applications of the latter. Continuing in this direction, a new estimator for the log-GW tail index and a related quantile estimator are introduced. Both are constructed using the Hill estimator as building block. Sufficient conditions for asymptotic normality are established. These results, together with the results of simulations and an application, indicate that the new estimator fulfils the potential of the log-GW tail limit as a widely applicable model for high quantile estimation, showing a substantial reduction in bias as well as improved precision when compared to an estimator based on the GP tail limit.

AB - The estimation of high quantiles for very low probabilities of exceedance pn much smaller than 1/n (with n the sample size) remains a major challenge. For this purpose, the log-Generalized Weibull (log-GW) tail limit was recently proposed as regularity condition as an alternative to the Generalized Pareto (GP) tail limit, in order to avoid potentially severe bias in applications of the latter. Continuing in this direction, a new estimator for the log-GW tail index and a related quantile estimator are introduced. Both are constructed using the Hill estimator as building block. Sufficient conditions for asymptotic normality are established. These results, together with the results of simulations and an application, indicate that the new estimator fulfils the potential of the log-GW tail limit as a widely applicable model for high quantile estimation, showing a substantial reduction in bias as well as improved precision when compared to an estimator based on the GP tail limit.

KW - High quantile

KW - Hill estimator

KW - Log-generalized Weibull tail limit

KW - Log-GW tail index

U2 - 10.1016/j.ecosta.2017.03.001

DO - 10.1016/j.ecosta.2017.03.001

M3 - Article

VL - 6

SP - 107

EP - 128

JO - Econometrics and Statistics

JF - Econometrics and Statistics

SN - 2468-0389

ER -

ID: 30800907