金融市场中极值指标的位移尺度不变估计  

Shift and Scale Invariant Estimation of Extreme Value Index in Finance Market

作　　者：李秀敏[1] 蔡霞[1] 

机构地区：[1]河北科技大学理学院,河北石家庄050018

出　　处：《数学的实践与认识》2013年第14期231-237,共7页Mathematics in Practice and Theory

基　　金：河北省科技厅软科学计划项目(12457203D-53);河北科技大学理工学院教育教学研究基金(2011Z08)

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.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.

关 键 词：极值理论 极值指标 参数估计 位移尺度不变估计 

分 类 号：O211.4[理学—概率论与数理统计] F832[理学—数学]