[1]陈向红,杨纪龙.正规变化重尾分布尾部指数的Crovella估计的强相合性[J].南京师大学报(自然科学版),2007,30(03):26-30.
　Chen Xianghong,Yang Jilong.Strong Consistency of Crovella Estimation for the Tail Index of Regular Variation Heavy-Tailed Distribution[J].Journal of Nanjing Normal University(Natural Science Edition),2007,30(03):26-30.
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正规变化重尾分布尾部指数的Crovella估计的强相合性()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第30卷
期数:
2007年03期
页码:
26-30
栏目:
数学
出版日期:
2007-09-30

文章信息/Info

Title:
Strong Consistency of Crovella Estimation for the Tail Index of Regular Variation Heavy-Tailed Distribution
作者:
陈向红;杨纪龙;
南京师范大学数学与计算机科学学院, 江苏南京210097
Author(s):
Chen Xianghong; Yang Jilong
School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China
关键词:
正规变化;  重尾分布;  尾部指数;  Crovella估计;  强相合性
Keywords:
regular var ia tion;  heavy-ta iled distributions;  ta il index;  Crov ella estim a tion;  strong cons is tency
分类号:
O211
摘要:
正规变化重尾分布的尾部指数的估计方法有很多种,但都不同程度地存在一定的局限性.为此,Crov-ella提出了一种从标度特征方面来估计尾部指数的方法,该方法易于应用,估计结果也比较准确.本文在阐述了该估计方法的具体步骤后,给出了相应的估计量,并证明了该估计量具有强相合性.
Abstract:
The estim ation o f ta il index fo r regular va riation heavy-ta iled distributions aroused ou r concern, m any scho lars proposed several m ethods, but all of them have som e disadvantages. C rove lla presented a new m ethod based on the scaling properties of sum s o f heavy-ta iled random variab les. It has the advantages o f being easy to app ly, and o f be ing re la tive ly accurate. In th is paper, the estim ation presented by C rove lla is desc ribed, and tha t the Crove lla estim ato r has strong consistency is proved.

参考文献/References:

[ 1]  H ill BM. A simp le genera l approach to infe rence about the ta il of a d istr ibution[ J]. Ann S tatist, 1975, 3: 1 163-1 174.
[ 2]  H a ll P G. Using the boo tstarp to estim ate m ean squard error and se lect sm ooth ing param eter in nonparam etric prob lem s[ J]. JM ultivariate Ann, 1990, 32: 177-203.
[ 3]  Ronald Hu ism an. Ta il-Index estim ate in sm a ll samp les[ J]. Journal o f Bus iness& Econom ic Statistics, 2001, 19: 208-216.
[ 4]  Be irlant J, Gu illou A. Pareto index estim ation underm ode rate right censor ing[ J]. Scand A Ctua J, 2001, 2: 111-125.
[ 5]  Gom esM I, O liveiraO. Censo ring estim ato rs o f a pos itive ta il index[ J]. Sta tistic and Probability Lette rs, 2003, 65: 147-159.
[ 6]  CrovellaM E, TaqquM S. Estim ating the heavy ta il index from sca ling properties[ J] . M e thodo logy and Com puting in Applide Probability, 1999, 1: 55-79.
[ 7]  Gabrie lK lam bauer. 数学分析[M ] . 孙本旺, 译. 长沙: 湖南人民出版社, 1981.

备注/Memo

备注/Memo:
作者简介: 陈向红( 1980- ) , 女, 硕士研究生, 主要从事概率统计的学习与研究.
通讯联系人: 杨纪龙( 1947- ) , 副教授, 主要从事随机积分和期权定价的教学与研究. E-m ail:yang jilong@ n jnu. edu. cn
更新日期/Last Update: 2013-05-05