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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.
In the theory of extreme value statistics, the extremum index determines the type of distribution, and Hill estimation has been widely used especially when the extremum index is greater than 0. However, the displacement invariance is not reflected in the Hill estimate, which is also the application Hill estimates. This improved estimate of Hill has a scale-invariance of displacement. The feasibility of the improved Hill estimator is studied through the comparison of several models and the empirical analysis of extreme indicators in financial markets.