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修正的Pickands估计样本点分割的自助估计方法 被引量：1

Using a Bootstrap Method to Choose the Sample Fraction in Modified Pickands Estimation
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摘要 在本文中,我们着重研究了极值指数的修正的Pickands型估计的样本点分割方法．我们在渐近二阶矩最小的准则下,利用子样本自助法给出了修正的Pickands型估计的样本点分割方法,从理论上证明了该估计的大样本性质,说明了这种分割在渐近二阶矩最小的准则下是渐近最优分割,同时提出了自适应的样本点分割的自助算法． In this paper, the optimality problem of sample fraction in modified Pickands estimation is studied. Under the asymptotic second moment principle, recurring to subsample bootstrap method, we solve the optimality problem of sample fraction in modified Pickands estimation, and prove the limit properties, illuminate our sample fraction is optimal under the asymptotic second moment principle. Simultaneity, an adaptive bootstrap procedure is given.
作者 欧阳资生 吴喜之
机构地区 湖南大学工商管理学院 中国人民大学统计学院
出处 《应用数学学报》 CSCD 北大核心 2006年第2期254-265,共12页 Acta Mathematicae Applicatae Sinica
基金 国家社会科学基金(编号:04BTJ010)湖南省自然科学基金(编号:05JJ40106)资助项目
关键词 极值指数 Pickands估计 自助法 extreme value index Pickands estimation, bootstrap
分类号 O212.7 [理学—概率论与数理统计]
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参考文献12

  • 1Pickands J. Statistical Inference Using Extreme order Statistics. Ann. Statist, 1975, 3:119-131.
  • 2Pereira T T. Second order Behavior of Domains of Attraction and the Bias of Generalized Pickands Estimator. Extreme Value Theory and Applications Ⅲ (eds. Lechner, J). Proc Gaithersburg Conference (NIST special publ), 1993.
  • 3Falk M. Efficiency of Convex Combinations of Pickands Estimator of the Extreme Value Index. J.Nonparametric Statist, 1994, 4. 133-147.
  • 4Drees H. Refined Pickands Estimators of the Extreme Value Index. Annals of Statistics, 1995, 17:1833-1855.
  • 5Yun S S. A Class of Pickands-type Estimatiors for the Extreme Value Index. J. of Statistical Planning and Inference, 2000, 83:113-124.
  • 6Yun S S. On a Generalized Pickands Estimator of Extreme Value Index. J, of Statistical Planning and Inference, 2002, 102:389-409.
  • 7Danielsson J. Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation.Journal of Multivariate Analysis, 1985, 76: 226-248.
  • 8Draisma G, Pereira T T. A Bootstrap-based Method to Achieve Optimality in Estimating the Extremevalue Index. Extremes, 1999, 2(4): 367-404.
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  • 10Geluk J, De Hall L. Regular Variation Extensions and Tauberian Theorems. Technical Report CWI Tract 40, CWI, Amsterdam, 1987.

同被引文献17

  • 1王剑峰,宋松柏.广义Pareto分布在超定量洪水序列频率分析中的应用[J].西北农林科技大学学报（自然科学版）,2010,38(2):191-196. 被引量：16
  • 2刘维奇,邢红卫.重尾分布尾指数估计研究进展[J].山西大学学报（自然科学版）,2012,35(2):163-173. 被引量：5
  • 3Fisher R A, Tippett L H C. Limiting forms of the frequency distribution of the largest or smallest members of a sample [J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1928, 24(1): 180-190.
  • 4Pickands J. Statistical Inference Using Extreme Order Statistics[J]. The Annals of Statistics, 1975, 3(1): 119-131.
  • 5Efron B. Bootstrap methods: another look at the Jackknife [J]. The Annals of Statistics, 1979, 7(1): 1-26.
  • 6Danielsson J. Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation [J]. Journal of Multivariate Analysis, 1985,76(1): 226-248.
  • 7Yun S S. A Class of pickands-type estimatiors for the extreme value index [J]. Journal of Statistical Planning and Inference, 2000, 83(1): 113-124.
  • 8Hosking J R M. L- moment- analysis and estimation of distributions using linear combinations of order- statistics [J]. Journal of the Royal Statistical Society,Series B (Methodological), 1990, 52(I): 105-124.
  • 9彭作祥.Pickands型估计的推广[J].数学学报（中文版）,1997,40(5):759-762. 被引量：12
  • 10程炳岩,丁裕国,张金铃,江志红.广义帕雷托分布在重庆暴雨强降水研究中的应用[J].高原气象,2008,27(5):1004-1009. 被引量：33

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应用数学学报
2006年 第2期

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