| 分布函数尾端点估计量的渐近性质 |
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| 引用本文： | 陶宝,彭作祥. 分布函数尾端点估计量的渐近性质[J]. 应用数学学报, 2007, 30(4): 615-624 |
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| 作者姓名： | 陶宝 彭作祥 |
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| 作者单位： | 1. 重庆工商大学理学院,重庆,400067
2. 西南大学数学与统计学院,重庆,400715 |
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| 基金项目： | 国家自然科学基金;重庆市教委资助项目 |
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| 摘 要： | 当极值指标小于0时,本文给出了分布函数F(x)的尾端点估计量,证明了该估计量的强相合性和弱相合性;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,证明了渐近正态性,进而可以构造F(x)的尾端点的渐近置信区间.
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| 关 键 词： | 极值指标 尾端点估计 强收敛速度 渐近正态性 |
| 修稿时间： | 2005-03-14 |
Asymptotic Properties of the Endpoint Estimators of a Distribution |
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| TAO BAO,PENG ZUOXIANG. Asymptotic Properties of the Endpoint Estimators of a Distribution[J]. Acta Mathematicae Applicatae Sinica, 2007, 30(4): 615-624 |
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| Authors: | TAO BAO PENG ZUOXIANG |
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| Affiliation: | 1,College of Science, Chongqing Technology and Business University, Chongqing 400067;2,School of Mathematics and Statistics, Southwest University, Chongqing 400715 |
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| Abstract: | In this paper,the authors give the endpoint estimators of a distribution func- tion F(x)as the extreme value index (?)<0.Their weak and strong consistency are proved. Under the second order regularly varing condition,their strong convergence rate and asymp- totic normality are derived by controling the convergence rate of regularly raring function. Moreover,the results may construct an asymptotic confidence interval for the endpoint estimators of a distribution function F(x). |
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| Keywords: | extreme value index endpoint estimator strong convergence rate asymptotic normality |
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