数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 611-618.

• 论文 • 上一篇    下一篇

负极值指标估计量的渐近性质

陶宝   

  1. 重庆工商大学 数学与统计学院 重庆 400067
  • 收稿日期:2011-04-19 修回日期:2013-11-22 出版日期:2014-06-25 发布日期:2014-06-25
  • 基金资助:

    国家自然科学基金(11101452)和重庆市教委科学技术研究项目(KJ100726)资助

Asymptotic Properties of the Negative Extreme-value Index Estimator

 TAO Bao   

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
  • Received:2011-04-19 Revised:2013-11-22 Online:2014-06-25 Published:2014-06-25
  • Supported by:

    国家自然科学基金(11101452)和重庆市教委科学技术研究项目(KJ100726)资助

摘要:

当极值指标小于0时, 该文提出了一种负极值指标估计量, 证明了该估计量的弱相合性和强相合性; 在二阶正规变化条件下,
通过限制正规变化函数的收敛速度, 给出了强收敛速度和渐近展式, 证明了渐近正态性, 并对平滑参数的最优选择进行了讨论.

关键词: 负极值指标, 弱相合性, 强相合性, 强收敛速度, 渐近展式

Abstract:

As the extreme-value index is negative, the author proposes the negative extreme-value index estimator, whose weak and strong consistency are proved.  Under the second order regularly varying condition, the author obtains the rate of strong convergence, asymptotic expansion and proves asymptotic normality. Moreover, the optimal choice of the smoothing parameter is discussed.

Key words: Negative extreme-value index, Weak consistency, Strong consistency, Rate of strong convergence, Asymptotic , expansion

中图分类号: 

  • 62G32