摘要
重尾分布可以很好地解释资产价格,收入分配,水文地质,社交媒体等经济,自然与社会现象,准确估计极值指数成为重尾分布应用的关键技术,1975年Hill估计的提出开辟了极值指数估计的先河,直到今天极值指数的估计仍是重尾建模的重点.为克服已有估计中存在的位置变化和渐近性的不足,借用统计量M_n^((α))(k_0,k)的渐近展式提出了一类新的位置不变极值指数估计(NLIE),在二阶正则变化条件下研究了其渐近展式以及阈值的最优选取,通过Monte-Carlo对NLIE与Fraga Alves所提的经典位置不变估计量γ_n^H(k_0,k)进行了模拟比较.结果表明,NLIE的效果更好.
Heavy-tailed distribution can well explain the economic, natural and social phenomena such as asset prices, income distribution, hydro-geology, social media, etc. Accurate estimation of extreme value index is a key technique for application of heavy-tailed distribution. The Hill estimator, introduced in 1975, which opened a precedent of estimating extreme value index, is still the focus of heavy-tailed modeling up to now. In order to overcome the shortcomings of the location variation and asymptotic behavior of the existing estimators, borrowing the asymptotic expansion of statistic M（？） n （k0; k）, this paper proposes a new kind of location invariant extreme value index estimator （NLIE） and studies its asymptotic expansion under second order regular variation. The optimal choice of threshold is discussed as well. The NLIE is compared with the classical location invariant estimator ^°H n （k0; k） by Monte-Carlo. The results show that NlIE behaves better than ^°H n （k0; k）.
作者
刘维奇
梁珊珊
LIU Wei-qi1，3, LIANG Shan-shan2(1. Research Center for Management and Decision Making, Shanxi University, Taiyuan 030006,China;2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China;3. Faculty of Finance and Banking, Shanxi University of Finance and Economics, Taiyuan 030006,Chin)
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2018年第2期179-190,共12页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家社会科学基金(15BJY164)
教育部人文社会科学基金(14YJA790034)
关键词
重尾分布
极值指数
位置不变
正则变化
渐近性质
heavy-tailed distribution
extreme value index
location invariant
regular variation
asymptotic property
