TY - JOUR
T1 - On multivariate separating Hill estimator under estimated location and scatter
AU - Heikkilä, Matias
AU - Dominicy, Yves
AU - Ilmonen, Pauliina
PY - 2018/11/20
Y1 - 2018/11/20
N2 - We consider estimating the tail-index of a distribution under the assumption of multivariate ellipticity. Recently, a separating Hill estimator for multivariate elliptical distributions was proposed. This estimator is an affine invariant alternative to using the marginal observations in tail-index estimation and is hence unaffected by, e.g. change of units of measurement. However, the separating Hill estimator depends on the location and scatter of the elliptical distribution, which, in practice, have to be estimated. The effect of replacing the true location and scatter of the distribution by estimates has previously been only examined through simulations. In this article we show that the error caused by replacing the location and scatter of the distribution by estimates indeed is asymptotically negligible. This fact is essential for the practicality of the separating Hill estimator. In addition to providing the theoretical results, we present simulation results on the asymptotic behaviour of the estimators.
AB - We consider estimating the tail-index of a distribution under the assumption of multivariate ellipticity. Recently, a separating Hill estimator for multivariate elliptical distributions was proposed. This estimator is an affine invariant alternative to using the marginal observations in tail-index estimation and is hence unaffected by, e.g. change of units of measurement. However, the separating Hill estimator depends on the location and scatter of the elliptical distribution, which, in practice, have to be estimated. The effect of replacing the true location and scatter of the distribution by estimates has previously been only examined through simulations. In this article we show that the error caused by replacing the location and scatter of the distribution by estimates indeed is asymptotically negligible. This fact is essential for the practicality of the separating Hill estimator. In addition to providing the theoretical results, we present simulation results on the asymptotic behaviour of the estimators.
KW - 62G32
KW - 62H12
KW - elliptical distribution
KW - extreme value index
KW - Multivariate extreme value theory
UR - http://www.scopus.com/inward/record.url?scp=85057343597&partnerID=8YFLogxK
U2 - 10.1080/02331888.2018.1548016
DO - 10.1080/02331888.2018.1548016
M3 - Article
AN - SCOPUS:85057343597
SP - 1
EP - 20
JO - STATISTICS
JF - STATISTICS
SN - 0233-1888
ER -