【作者】 王淑良；

【导师】 彭作祥；

【作者基本信息】 西南大学 ， 概率论与数理统计， 2007， 硕士

【摘要】 设{X_n，n≥1}为独立同分布随机变量序列，公共分布函数为F（x）．X-（（1，n））≤X_（2，n）≤…≤X_（n，n）为X₁，X₂，…，X_n的顺序统计量．若存在α_n＞0，b_n∈R，γ∈R和非退化分布函数G_γ（x），使得当n→∞时则称G_γ（x）为广义极值分布函数．此时称分布函数F（x）属于吸引场G_γ（x），γ称为极值指数，记为F∈D（G_γ）．当分布函数未知时对极值指数，γ的估计构成了极值理论的重要组成部分．本文在矩型估计量的基础上提出了一类新的矩型估计量其中且k=k（n）→∞，k（n）／n→0．本文的第一部分讨论了其强弱相合性，并在一定条件下证明了它的渐近正态性，第二部分在二阶正规变换条件下讨论了估计量的展开及分布的渐近正态展开，最后通过随机模拟对新的估计量和矩型估计量进行了模拟比较分析．更多还原

【Abstract】 Let {X_i, 1≤i≤n} bc an independent identically distributed random variables with common distribution F（x）, and X_l,n≤X_2,n≤…X_n,n be the associated order statistics of X₁, X₂…, X_n. It is well known that if there exist constants an＞O, b_n∈R, such thatG_γ（x） is called extreme value distribution with extreme value indexγ, and F（x） is said to be in the domains of attractions of G_γ（x）, denoted as F∈D（G_γ）. Estimating the parameterγ, has become an important part in extreme value theory as F（x） is unknown. In this paper, a new kind of moment-type estimator is proposed,denotcd aswhereandThe arrangement of this thesis is: In the first part of this paper, asymptotic properties such as weak and strong consistency and asymptotic distribution ofγ_n have been considered under some weakly conditions. The expansions ofγ_n and its distribution are discussed in the second part under second regular variation conditions. Lastly some comparison ofγ_n and Moment type extreme value index estimator provided by Dekkers and de Haan are given by Monte Carlo Simulation.Keywords: Moment estimator; regular varying function; Weak and strong consistency; asymptotic normality; order statistics更多还原