适度删失时的极值指数估计

Extreme value index estimation under moderate right censoring

讨论在实际中常常会碰到的删失数据情形下的极值指数估计问题.限于极值数据本来就不多,将删失限定为适度删失.构造了适度右删失时Pareto型分布的一个子族—Hall族的极值指数的估计量.借助于估计量的信息,巧妙地构造了加权二乘估计的权数.从理论上说明了加权二乘估计的可行性,并利用MC方法,对Burr(1,1,1)、Burr(1,0.5,2)、Fréchet(1)、Fréchet(2)、学生-t1、学生-t4等几种常见的极值分布进行模拟,说明了加权二乘估计方法对门限值的选取并不敏感,具有很好的稳健性.同时,将利用Burr(1,1,1)、Burr(1,0.5,2)、Fréchet(1)分布模拟所得结果与Beirlant等人(2001)利用指数回归模型所得结果进行比较,说明了新方法比指数回归模型更为理想.

The paper discusses extreme value index estimation under moderate right censoring.Because of the limited number of data,only the moderate right censoring is studied.An extreme value index estimator of Hall class in Pareto-type distribution is put forward in small samples under moderate right censoring.Recurring to information obtained from estimators,the weight used in least square method is constructed and the feasibillity of the weighted least square method is proved.By MC simulation,it concludes that the method is quite robust with respect to the choice of threshold for small samples case.In the end of this paper,the result based on simulating the distribution of Burr(1,1,1),Burr(1,0.5,2) and Fréchet(1) is compared with and proved berter than that of the exponential regression model method.(Beirlant J et al,2001) under moderate right censoring.