Multivariate extremes based on a notion of radius

Modeling and understanding multivariate extreme events is challenging, but of great importance invarious applications— e.g. in biostatistics, climatology, and finance. The separating Hill estimator canbe used in estimating the extreme value index of a heavy tailed multivariate elliptical distribution. Weconsider the asymptotic behavior of the separating Hill estimator under estimated location and scatter.The asymptotic properties of the separating Hill estimator are known under elliptical distribution withknown location and scatter. However, the effect of estimation of the location and scatter has previouslybeen examined only in a simulation study. We show, analytically, that the separating Hill estimator isconsistent and asymptotically normal under estimated location and scatter, when certain mild conditionsare met.