TY - JOUR
T1 - A location-invariant probability weighted moment estimation of the Extreme Value Index
AU - Caeiro, Frederico Almeida Gião Gonçalves
AU - Gomes, M. Ivette
AU - Henriques-Rodrigues, Lígia
N1 - Fundacao para a Ciencia e a Tecnologia (PEst-OE/MAT/UI0006/2014
PEst-OE/MAT/UI0297/2014)
PTDC/FEDER (SFRH/BPD/77319/2011)
PY - 2016/4/2
Y1 - 2016/4/2
N2 - The peaks over random threshold (PORT) methodology and the Pareto probability weighted moments (PPWM) of the largest observations are used to build a class of location-invariant estimators of the Extreme Value Index (EVI), the primary parameter in statistics of extremes. The asymptotic behaviour of such a class of EVI-estimators, the so-called PORT-PPWM EVI-estimators, is derived, and an alternative class of location-invariant EVI-estimators, the generalized Pareto probability weighted moments (GPPWM) EVI-estimators is considered as an alternative. These two classes of estimators, the PORT-PPWM and the GPPWM, jointly with the classical Hill EVI-estimator and a recent class of minimum-variance reduced-bias estimators are compared for finite samples, through a large-scale Monte-Carlo simulation study. An adaptive choice of the tuning parameters under play is put forward and applied to simulated and real data sets.
AB - The peaks over random threshold (PORT) methodology and the Pareto probability weighted moments (PPWM) of the largest observations are used to build a class of location-invariant estimators of the Extreme Value Index (EVI), the primary parameter in statistics of extremes. The asymptotic behaviour of such a class of EVI-estimators, the so-called PORT-PPWM EVI-estimators, is derived, and an alternative class of location-invariant EVI-estimators, the generalized Pareto probability weighted moments (GPPWM) EVI-estimators is considered as an alternative. These two classes of estimators, the PORT-PPWM and the GPPWM, jointly with the classical Hill EVI-estimator and a recent class of minimum-variance reduced-bias estimators are compared for finite samples, through a large-scale Monte-Carlo simulation study. An adaptive choice of the tuning parameters under play is put forward and applied to simulated and real data sets.
KW - adaptive semi-parametric estimation
KW - asymptotic properties
KW - bootstrap methodology
KW - Extreme Value Index
KW - heavy tails
KW - location/scale-invariant estimation
KW - Monte-Carlo simulation
KW - statistics of extremes
UR - http://www.scopus.com/inward/record.url?scp=84909952827&partnerID=8YFLogxK
U2 - 10.1080/00207160.2014.975217
DO - 10.1080/00207160.2014.975217
M3 - Article
AN - SCOPUS:84909952827
SN - 0020-7160
VL - 93
SP - 676
EP - 695
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
IS - 4
ER -