摘要：The extreme-value index γ is an important parameter in extreme-value theory sinceit controls the first order behavior of the distribution tail. In the literature, numerousestimators of this parameter have been proposed especially in the case of heavy-taileddistributions, which is the situation considered here. Most of these estimators dependon the k largest observations of the underlying sample. Their bias is controlled by thesecond order parameter ρ. In order to reduce the bias of γ's estimators or to select thebest number k of observations to use, the knowledge of ρ is essential. In this pap er,we prop ose a simple approach to estimate the second order parameter ρ leading toboth existing and new estimators. We establish a general result that can be used toeasily prove the asymptotic normality of a large number of estimators proposed in theliterature or to compare di.erent estimators within a given family. Some illustrationson simulations are also provided
关键词：extreme-value theory; heavy-tailed distribution; extreme-value index; second order;parameter; asymptotic properties
