重尾指数估计中阈值k的简便优化估计  

Simple and optimized choice of the threshold for heavy-tailed index estimation

作　　者：刘维奇[1,2] 邢红卫[2] 

机构地区：[1]山西大学管理科学与工程研究所,太原030006 [2]山西大学数学科学学院,太原030006

出　　处：《系统工程理论与实践》2010年第8期1465-1470,共6页Systems Engineering-Theory & Practice

基　　金：教育部人文社会科学研究项目(07JA630027;06JA630035);山西省高校人文社科重点研究基地项目(20083006)

摘　　要：重尾分布在风险管理和金融领域有极为重要的应用价值.提出了一种选取重尾指数估计阈值k的解析方法,称为简便优化估计.并且利用Hill估计和已知重尾分布进行Monte-Carlo模拟,发现简便优化方法与Sum-plot方法和Bootstrap方法具有同样的精确性与稳健性,三种方法都能得到令人满意的结果.简便优化方法在精确性方面似乎略占优势,计算方法简单,且不受分布类型和重尾指数范围的影响,在分布为Pareto型时基于简便优化方法的Hill估计依然具有相合性.Heavy-tailed distribution models have revealed to be quite useful in fields such as risk management and finance.We provide an analytical method of choosing threshold for heavy-tailed index estimation, named Simple and Optimized Estimator（SOE）.Then we proceed to an intensive computer simulation that enables us to find,through Monte-Carlo techniques,the SOE method is accurate and robust as well as Sum-plot method and Bootstrap method,the three methods can derive satisfactory results.The SOE method seems to have a slight advantage in terms of accuracy,the calculation method is simple,but not be affected by the types of the heavy-tailed distributions and the scope of the index,the Hill estimator based on the SOE method is still consistent whenever the distributions are Pareto-type models.

关 键 词：Hill估计 Sum-plot方法 BOOTSTRAP方法 简便优化方法 相合性 

分 类 号：O211.9[理学—概率论与数理统计]