【摘要】 在极值统计理论中,极值指标决定着分布的类型.特别是当极值指标大于零时,Hill估计一直得到较为广泛的应用.然而,位移不变性没有在Hill估计中体现,这也是应用Hill估计的限制.应用一个改进的Hill估计,这个估计具有位移尺度不变性.通过对几种模型的模拟比较和对金融市场中极值指标的实证分析,研究了改进的Hill估计的可行性.更多还原

【Abstract】 The extreme value index rules the type of a distribution function in extreme value theory.The Hill estimator has been largely used in order to estimate the parameter associated to a distribution function with a positive index.One of the criticisms to this estimator is the fact it is not location invariant,which restricts its application.In this paper,a new Hill estimator is studied,which is location invariant.And also the bias of the estimation is reduced.A comparative simulation study is presented for several models.And the empirical results in finance market show that this new Hill estimator is appropriate.更多还原