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1.
极值分布指数的Pickands估计的渐近正态性   总被引:2,自引:0,他引:2  
本文中,我们在很弱的条件下证明了极值分布形状参数的Rickands估计的渐近正态性.改进了Dekkers和DeHaan在1989年给出的结果.另外,我们得到了几个关于正规变化函数的结果.  相似文献   

2.
考虑响应变量随机缺失情形下的非线性EV模型.给出了未知参数的降维估计,有效避免了高维核估计带来的维数灾祸问题.所构造的统计量渐近于x~2分布,所得结果可以用来构造未知参数的置信域.  相似文献   

3.
成分数据的几个估计   总被引:2,自引:0,他引:2  
本文用SURE模型导出了成分数据的均值和协差阵的估计。特别地,在成分数据服从Dirichlet分布D(a1,…,ad 1)时,构造了参数a=∑j=1^d 1 aj的二次估计及a1,…,ad 1的三次估计,求出了这些估计的渐近分布。  相似文献   

4.
三参数广义帕累托分布的似然矩估计   总被引:1,自引:0,他引:1  
广义帕累托分布(GPD)在极值统计的POT模型中常常被用来逼近超过阈值u的超出量X_i-u的分布. 为解决经典估计方法存在的问题, Zhang (Zhang J, Likelihood moment estimation for the generalized Pareto distribution, Aust N Z J Stat, 2007, 49:69--77) 对两参数GPD (GP2)提出一种新的估计方法------似然矩估计(LM), 它容易计算且具有较高的渐近有效性. 本文将此方法从两参数的情形推广到三参数GPD (GP3), 结果表明尺度参数和形状参数估计的渐近性质与以上所提到的文章完全相同. 针对GP3的LM估计也具有总是存在、易于计算以及 对绝大多数的形状参数具有接近于最小的偏差和均方误差的特点.  相似文献   

5.
污染数据半参数回归模型估计的渐近正态性   总被引:1,自引:0,他引:1  
陈明华 《工科数学》1999,15(3):28-32
考虑半参数回归模型:yi=xiβ g(ti) e1,i=1,2,…,n,其中Ee1=0,Ee^2/1=δ2/1>0.假定y1,y2,…,y0受到另一独立同分布随机变量序列μ1,μ2,…,μn的污染,{μi}与{y1}独立,且仅能观察到污染数据.[ι]对由污染数据作出的参数β的估计βn,证明了它的强相合性.而本则证明了它的渐近正态性.  相似文献   

6.
指数分布族中矩估计序贯置信区间   总被引:1,自引:0,他引:1  
在矩估计的基础上,对于给定精度(2d)及置信系数(α),建立了对参数函数g(θ) 的一个序贯置信区间估计的程序.并讨论了在一定条件下,当d→0,它的渐近相合性、渐近有效性及有界的最优费用差(EN(d)-n(d))等渐近性质.  相似文献   

7.
序约束下ARCH(0,2)模型参数估计与检验   总被引:3,自引:0,他引:3  
本文研究了平稳ARCH(0,2)模型未知参数α的极大似然估计及有序约束时α的极大似然估计的渐近性质,给出了参数序关系(α1≥α2)的检验方法,并得出了似然比检验统计量的渐近分布。用二次规划的算法,给出求各种情况下参数α的极大似然估计的数值算法。  相似文献   

8.
二元极值分布混合模型的矩估计   总被引:1,自引:0,他引:1       下载免费PDF全文
极值理论在各个领域得到了越来越多的关注和应用, 尤其是多元极值分布. 而矩估计是一种经典的参数估计方法, 计算简单且具有某些优良性, 本文给出边缘为标准指数分布的二元极值混合模型相关参数的矩估计及其渐近方差. 并将其与极大似然估计的渐近方差比较, 结果表明矩估计是一个较好的估计.  相似文献   

9.
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.  相似文献   

10.
考虑一带有异方差的固定设计部分线性回归模型yij=X'ijβ+g(tij)+εij,i=1,2…,k:j=1,2,…,ni,和sum from i=1 to kni=n,其中yij为响应变量,β=(β1,…,βp)’是未知的参数向量,g(·)是未知的函数,Xij=(Xij1,…,Xijp)’和tij∈[0,1]为已知的非随机设计点,εij为均值0,方差是σi2的随机误差,其中σi2可能不同.通过B样条级数近似非参数分量,构造了参数分量β的一个半参数广义最小二乘估计.在一些矩条件下,导出了此半参数广义最小二乘估计的渐近分布,大多数在实际中遇到的误差分布都满足这些矩条件.另外,也构造了半参数广义最小二乘估计的渐近协方差矩阵的一个相合估计,还讨论了非参数分量的B样条估计.所有这些大样本性质都是在k趋于无穷大,ni有限时导出的.这些结果能被用来做渐近有效的统计推导.  相似文献   

11.
在本文中, 我们构造了一种新的极值分位数估计, 给出了估计量的极限性质. 同时, 在渐近二阶矩最小的准则下, 利用子样本自助法给出了计算所构造的极值分位数估计时的样本点分割方法, 从理论上证明了这一极限结果, 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.  相似文献   

12.
Smith (1994) introduced the idea of extreme regression quantiles and he developed some asymptotic results for algebraically tailed error distributions. The results provided a close analogy to standard extreme value theory for one-sample extremes. Here we obtain the following generalizations. First, an extreme value distribution theory is developed in the exponentially tailed case, where the extreme slope estimates need not diverge to infinity and may actually be consistent. The design conditions of Smith (1994) are also generalized. Second, the tail behavior measure of Jureckova´ (1981) and He et al. (1990) is considered for extreme quantiles. For algebraically tailed error distributions, the average right extreme regression fit acts like a one-sample right extreme; while in the exponentially tailed case, the tail behavior is more like that of a slightly more central order statistic.  相似文献   

13.
This paper considers multivariate extreme value distribution in a nested logistic model. The dependence structure for this model is discussed. We find a useful transformation that transformed variables possess the mixed independence. Thus, the explicit algebraic formulae for a characteristic function and moments may be given. We use the method of moments to derive estimators of the dependence parameters and investigate the properties of these estimators in large samples via asymptotic theory and in finite samples via computer simulation. We also compare moment estimation with a maximum likelihood estimation in finite sample sizes. The results indicate that moment estimation is good for all practical purposes.  相似文献   

14.
This paper deals with the estimation of the extreme value index in local extreme value models. We establish local asymptotic normality (LAN) under certain extreme value alternatives. It turns out that the central sequence occurring in the LAN expansion of the likelihood process is up to a rescaling procedure the Hill estimator. The central sequence plays a crucial role for the construction of asymptotic optimal statistical procedures. In particular, the Hill estimator is asymptotically minimax.  相似文献   

15.
Summary Denote byH ak-dimensional extreme value distribution with marginal distributionH i (x)=Λ(x)=exp(−e x ),xR 1. Then it is proved thatH(x)=Λ(x 1)...Λ(x k ) for anyx=(x 1, ...,x k ) ∈R k , if and only if the equation holds forx=(0,...,0). Next some multivariate extensions of the results by Resnick (1971,J. Appl. Probab.,8, 136–156) on tail equivalence and asymptotic distributions of extremes are established.  相似文献   

16.
Bayesian Inference for Extremes: Accounting for the Three Extremal Types   总被引:2,自引:0,他引:2  
The Extremal Types Theorem identifies three distinct types of extremal behaviour. Two different strategies for statistical inference for extreme values have been developed to exploit this asymptotic representation. One strategy uses a model for which the three types are combined into a unified parametric family with the shape parameter of the family determining the type: positive (Fréchet), zero (Gumbel), and negative (negative Weibull). This form of approach never selects the Gumbel type as that type is reduced to a single point in a continuous parameter space. The other strategy first selects the extremal type, based on hypothesis tests, and then estimates the best fitting model within the selected type. Such approaches ignore the uncertainty of the choice of extremal type on the subsequent inference. We overcome these deficiencies by applying the Bayesian inferential framework to an extended model which explicitly allocates a non-zero probability to the Gumbel type. Application of our procedure suggests that the effect of incorporating the knowledge of the Extremal Types Theorem into the inference for extreme values is to reduce uncertainty, with the degree of reduction depending on the shape parameter of the true extremal distribution and the prior weight given to the Gumbel type.  相似文献   

17.
The asymptotic expansions for the distribution functions of Pickands-type estimators in extreme statistics are obtained. In addition, several useful results on regular variation and intermediate order statistics are presented. Project supported by the National Natural Science Foundation of China (Grant No. 19601007) and Doctoral Program Foundation of Higher Education of China.  相似文献   

18.
The score tests of independence in multivariate extreme values derived by Tawn (Tawn, J.A., “Bivariate extreme value theory: models and estimation,” Biometrika 75, 397–415, 1988) and Ledford and Tawn (Ledford, A.W. and Tawn, J.A., “Statistics for near independence in multivariate extreme values,” Biometrika 83, 169–187, 1996) have non-regular properties that arise due to violations of the usual regularity conditions of maximum likelihood. Two distinct types of regularity violation are encountered in each of their likelihood frameworks: independence within the underlying model corresponding to a boundary point of the parameter space and the score function having an infinite second moment. For applications, the second form of regularity violation has the more important consequences, as it results in score statistics with non-standard normalisation and poor rates of convergence. The corresponding tests are difficult to use in practical situations because their asymptotic properties are unrepresentative of their behaviour for the sample sizes typical of applications, and extensive simulations may be needed in order to evaluate adequately their null distribution. Overcoming this difficulty is the primary focus of this paper. We propose a modification to the likelihood based approaches used by Tawn (Tawn, J.A., “Bivariate extreme value theory: models and estimation,” Biometrika 75, 397–415, 1988) and Ledford and Tawn (Ledford, A.W. and Tawn, J.A., “Statistics for near independence in multivariate extreme values,” Biometrika 83, 169–187, 1996) that provides asymptotically normal score tests of independence with regular normalisation and rapid convergence. The resulting tests are straightforward to implement and are beneficial in practical situations with realistic amounts of data. AMS 2000 Subject Classification Primary—60G70 Secondary—62H15  相似文献   

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