TY - JOUR
T1 - Parameter and quantile estimation for the generalized Pareto distribution in peaks over threshold framework
AU - Kang, Suyeon
AU - Song, Jongwoo
N1 - Funding Information:
This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2015S1A5B6036244).
Publisher Copyright:
© 2017 The Korean Statistical Society
PY - 2017/12
Y1 - 2017/12
N2 - In this article, we consider six estimation methods for extreme value modeling and compare their performances, focusing on the generalized Pareto distribution (GPD) in the peaks over threshold (POT) framework. Our goal is to identify the best method in various conditions via a thorough simulation study. In order to compare the estimators in the POT sense, we suggest proper strategies for some estimators originally not developed under the POT framework. The simulation results show that a nonlinear least squares (NLS) based estimator outperforms others in parameter estimation, but there is no clear winner in quantile estimation. For quantile estimation, NLS-based methods perform well even when the sample size is small and the Hill estimator comes to the front when the underlying distribution has a very heavy tail. Applications of EVT cover many different fields and researchers on each field may have their own experimental conditions or practical restrictions. We believe that our results would provide guidance on determining proper estimation method on future analysis.
AB - In this article, we consider six estimation methods for extreme value modeling and compare their performances, focusing on the generalized Pareto distribution (GPD) in the peaks over threshold (POT) framework. Our goal is to identify the best method in various conditions via a thorough simulation study. In order to compare the estimators in the POT sense, we suggest proper strategies for some estimators originally not developed under the POT framework. The simulation results show that a nonlinear least squares (NLS) based estimator outperforms others in parameter estimation, but there is no clear winner in quantile estimation. For quantile estimation, NLS-based methods perform well even when the sample size is small and the Hill estimator comes to the front when the underlying distribution has a very heavy tail. Applications of EVT cover many different fields and researchers on each field may have their own experimental conditions or practical restrictions. We believe that our results would provide guidance on determining proper estimation method on future analysis.
KW - Generalized Pareto distribution
KW - Hill estimator
KW - Maximum likelihood estimator
KW - Nonlinear least squares
KW - Peaks over threshold
UR - http://www.scopus.com/inward/record.url?scp=85019698845&partnerID=8YFLogxK
U2 - 10.1016/j.jkss.2017.02.003
DO - 10.1016/j.jkss.2017.02.003
M3 - Article
AN - SCOPUS:85019698845
VL - 46
SP - 487
EP - 501
JO - Journal of the Korean Statistical Society
JF - Journal of the Korean Statistical Society
SN - 1226-3192
IS - 4
ER -