【作者】 陈芝凯；

【导师】 张志强；

【作者基本信息】 华东师范大学 ， 概率论与数理统计， 2008， 硕士

【摘要】 近些年来,极值理论再次成为统计研究领域的热点。极值理论(ExtremeValue Theory)是研究顺序统计量的极端值的统计特性的建模与估计问题。以往的关于极值理论的文献都基本上是讨论了独立同分布情形下的极值理论,已经提出了大量的结果,形成了相对成熟的理论构架。近二十多年来,对平稳序列的极值理论的研究也开始多了起来,提出了很多极值指标θ的估计方法,但对于极值指标θ的假设检验问题的讨论并不是很多。本文在介绍了经典极值理论和平稳序列的基本极值理论之后,通过随机模拟法,验证了对于极值指标θ＜1的平稳同分布随机序列来说,溢出值时间间隔分布是不服从简单几何分布的。本文提出了对于极值指标θ＜1的平稳序列的溢出值时间间隔分布服从混合几何分布的假设检验问题,给出了检验统计量的渐近分布和拒绝域。此外,本文还讨论了检验功效问题,并以GARCH和ARMAX过程为例,讨论了检验的功效。更多还原

【Abstract】 Extreme Value Theory is a theory considering the behaviour of extreme values of a sequence. Before 1980s, a large number of papers appeared, mainly considered the Extreme Value Theory for indenpendent and identically distributed ( i.i.d. ) sequences. In the last two decades, Extreme Value theory for stationary time series attacted more and more interests, and varies of methods were developed to estimate the extremal index 6 for such sequences. However, few authors considered the hypothese testing problem on the extremal index. In this paper, we shortly introduce the classical extreme value theory and basic extreme value theory of stationary sequences. We investigate the inter-exceedance times of a stationary sequence, extremal indexθ<1, do not follow geometric distribution. We present a hypothesis test problem that the inter-exceedance times of a stationary sequence, extremal index 0<\, follow mixed geometric distribution. The asymptotic distribution of the test statistic and rejected domain are given. Test power is also discussed in the end. Test power of the sequences from GARCH process and ARMAX process are given via simulation.更多还原