Estimation of the third-order parameter in extreme value statistics

被引：0
作者：
Yuri Goegebeur
Tertius de Wet
机构：
[1] University of Southern Denmark,Department of Mathematics and Computer Science
[2] University of Stellenbosch,Department of Statistics and Actuarial Science
来源：
TEST | 2012年 / 21卷
关键词：
Pareto-type distribution; Third-order parameter; Fourth-order condition; 62G20; 62G30; 62G32;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We introduce a class of estimators for the third-order parameter in extreme value statistics when the distribution function underlying the data is heavy tailed. For appropriately chosen intermediate sequences of upper order statistics, consistency is established under the third-order tail condition and asymptotic normality under the fourth-order tail condition. Simulation experiments illustrate the finite sample behavior of some selected estimators.
引用
收藏
页码：330 / 354
页数：24
相关论文
共 56 条
[1]  
Beirlant J(1999)Tail index estimation and an exponential regression model Extremes 2 177-200
[2]  
Dierckx G(2002)On exponential representations of log-spacings of extreme order statistics Extremes 5 157-180
[3]  
Goegebeur Y(1998)Burr regression and portfolio segmentation Insur Math Econ 23 231-250
[4]  
Matthys G(1996)Tail index estimation, Pareto quantile plots, and regression diagnostics J Am Stat Assoc 91 1659-1667
[5]  
Beirlant J(2006)A new class of estimators of a “scale” second order parameter Extremes 9 193-211
[6]  
Dierckx G(2008)Minimum-variance reduced-bias tail index and high quantile estimation REVSTAT Stat J 6 1-20
[7]  
Guillou A(1967)Asymptotic distribution of linear combinations of functions of order statistics with applications to estimation Ann Math Stat 38 52-72
[8]  
Stărică C(2010)Semi-parametric estimation for heavy tailed distributions Extremes 13 55-87
[9]  
Beirlant J(1996)Generalized regular variation of second order J Aust Math Soc A 61 381-395
[10]  
Goegebeur Y(1998)Selecting the optimal sample fraction in univariate extreme value estimation Stoch Process Appl 75 149-172
123456