Details
| Original language | English |
|---|---|
| Pages (from-to) | 55 - 83 |
| Number of pages | 29 |
| Journal | Extremes |
| Volume | 23 |
| Issue number | 1 |
| Early online date | 5 Sept 2019 |
| Publication status | Published - Mar 2020 |
Abstract
In risk quantification of extreme events in multiple dimensions, a correct specification of the dependence structure among variables is difficult due to the limited size of effective data. This paper studies the problem of estimating quantiles for bivariate extreme value distributions, considering that an estimated Pickands dependence function may deviate from the truth within some fixed distance. Our method thus finds optimal upper and lower bounds for the true but unknown dependence function, based on which robust quantile bounds are obtained. A simulation study shows the usefulness of our robust estimates that can supplement traditional error estimation methods.
Keywords
- 60G70, 62G32, 62G35, 62H12, Bivariate quantile, Extremal dependence misspecification, Extreme value theory, Robust risk measure
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Engineering(all)
- Engineering (miscellaneous)
- Economics, Econometrics and Finance(all)
- Economics, Econometrics and Finance (miscellaneous)
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Extremes, Vol. 23, No. 1, 03.2020, p. 55 - 83.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - Robust quantile estimation under bivariate extreme value models
AU - Kim, Sojung
AU - Rye, Heelang
AU - Kim, Kyoung-Kuk
N1 - Funding information: The authors thank all the anonymous reviewers and the Editor-in-Chief, Thomas Mikosch, for comments and suggestions that helped improve and clarify this manuscript. The work of K. Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (NRF-2019R1A2C1003144).
PY - 2020/3
Y1 - 2020/3
N2 - In risk quantification of extreme events in multiple dimensions, a correct specification of the dependence structure among variables is difficult due to the limited size of effective data. This paper studies the problem of estimating quantiles for bivariate extreme value distributions, considering that an estimated Pickands dependence function may deviate from the truth within some fixed distance. Our method thus finds optimal upper and lower bounds for the true but unknown dependence function, based on which robust quantile bounds are obtained. A simulation study shows the usefulness of our robust estimates that can supplement traditional error estimation methods.
AB - In risk quantification of extreme events in multiple dimensions, a correct specification of the dependence structure among variables is difficult due to the limited size of effective data. This paper studies the problem of estimating quantiles for bivariate extreme value distributions, considering that an estimated Pickands dependence function may deviate from the truth within some fixed distance. Our method thus finds optimal upper and lower bounds for the true but unknown dependence function, based on which robust quantile bounds are obtained. A simulation study shows the usefulness of our robust estimates that can supplement traditional error estimation methods.
KW - 60G70
KW - 62G32
KW - 62G35
KW - 62H12
KW - Bivariate quantile
KW - Extremal dependence misspecification
KW - Extreme value theory
KW - Robust risk measure
UR - http://www.scopus.com/inward/record.url?scp=85073783995&partnerID=8YFLogxK
U2 - 10.1007/s10687-019-00362-2
DO - 10.1007/s10687-019-00362-2
M3 - Article
VL - 23
SP - 55
EP - 83
JO - Extremes
JF - Extremes
SN - 1386-1999
IS - 1
ER -