摘要
广义帕累托分布(GPD)在极值统计的POT模型中常常被用来逼近超过阈值u的超出量X_i-u的分布.为解决经典估计方法存在的问题,Zhang(Zhang J,Likelihood moment estimation for the generalized Pareto distribution,Aust N Z J Stat,2007,49:69-77)对两参数GPD(GP2)提出一种新的估计方法——似然矩估计(LM),它容易计算且具有较高的渐近有效性.本文将此方法从两参数的情形推广到三参数GPD(GP3),结果表明尺度参数和形状参数估计的渐近性质与以上所提到的文章完全相同.针对GP3的LM估计也具有总是存在、易于计算以及对绝大多数的形状参数具有接近于最小的偏差和均方误差的特点.
In the peaks-over-threshold （POT） model, the generalized Pareto distribution （GPD） is commonly used to fit the distribution of the excess Xi- u, where u is the threshold. Zhang （Zhang J, Likelihood moment estimation for the generalized Pareto distribution, Aust N Z J Star, 2007, 49：69-77） proposed a new estimation method--likelihood moment estimation （LM） for 2-parameter GPD, which is easy to compute and has high asymptotic efficiency with respect to the traditional methods. This method has been extended to 3- parameter GPD in the present paper. The result shows that the asymptotic property of estimators for scale and shape parameters is the same as that of Zhang. Moreover, the LM estimator for 3-parameter GPD always exists, is simple to compute and is close to the lowest bias and rose over a wide range of shape parameters.
出处
《数学年刊（A辑）》
CSCD
北大核心
2013年第3期299-312,共14页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10971143
No.11271033)
北京市教育委员会(No.KM200910028003
No.KM201110028003)的资助
关键词
广义帕累托分布
似然矩估计
渐近分布
极值数据
Generalized Pareto distribution, Likelihood moment estimation Asymptotic distribution, Extremal data
