TY - JOUR
T1 - Multivariate moment based extreme value index estimators
AU - Heikkilä, Matias
AU - Dominicy, Yves
AU - Ilmonen, Pauliina
PY - 2016/12
Y1 - 2016/12
N2 - Modeling extreme events is of paramount importance in various areas of science—biostatistics, climatology, finance, geology, and telecommunications, to name a few. Most of these application areas involve multivariate data. Estimation of the extreme value index plays a crucial role in modeling rare events. There is an affine invariant multivariate generalization of the well known Hill estimator—the separating Hill estimator. However, the Hill estimator is only suitable for heavy tailed distributions. As in the case of the separating multivariate Hill estimator, we consider estimation of the extreme value index under the assumptions of multivariate ellipticity and independent identically distributed observations. We provide affine invariant multivariate generalizations of the moment estimator and the mixed moment estimator. These estimators are suitable for both light and heavy tailed distributions. Asymptotic properties of the new extreme value index estimators are derived under multivariate elliptical distribution with known location and scatter. The effect of replacing true location and scatter by estimates is examined in a thorough simulation study. We also consider two data examples: one financial application and one meteorological application.
AB - Modeling extreme events is of paramount importance in various areas of science—biostatistics, climatology, finance, geology, and telecommunications, to name a few. Most of these application areas involve multivariate data. Estimation of the extreme value index plays a crucial role in modeling rare events. There is an affine invariant multivariate generalization of the well known Hill estimator—the separating Hill estimator. However, the Hill estimator is only suitable for heavy tailed distributions. As in the case of the separating multivariate Hill estimator, we consider estimation of the extreme value index under the assumptions of multivariate ellipticity and independent identically distributed observations. We provide affine invariant multivariate generalizations of the moment estimator and the mixed moment estimator. These estimators are suitable for both light and heavy tailed distributions. Asymptotic properties of the new extreme value index estimators are derived under multivariate elliptical distribution with known location and scatter. The effect of replacing true location and scatter by estimates is examined in a thorough simulation study. We also consider two data examples: one financial application and one meteorological application.
KW - Elliptical distribution
KW - Mixed moment estimator
KW - Moment estimator
UR - http://www.scopus.com/inward/record.url?scp=85006750997&partnerID=8YFLogxK
U2 - 10.1007/s00180-016-0706-y
DO - 10.1007/s00180-016-0706-y
M3 - Article
AN - SCOPUS:85006750997
SN - 0943-4062
VL - 32
SP - 1481
EP - 1513
JO - Computational Statistics
JF - Computational Statistics
IS - 4
ER -