共查询到18条相似文献,搜索用时 66 毫秒
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
潘家柱 《数学年刊A辑(中文版)》1995,(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.
刘强 《数学的实践与认识》2011,41(10)
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.
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
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.
7.
8.
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.
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.
Moment Estimation for Multivariate Extreme Value Distribution in a Nested Logistic Model 总被引:5,自引:0,他引:5
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.
Frank Marohn 《Annals of the Institute of Statistical Mathematics》1997,49(4):645-666
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.
Rinya Takahashi 《Annals of the Institute of Statistical Mathematics》1987,39(1):637-647
Summary Denote byH ak-dimensional extreme value distribution with marginal distributionH
i
(x)=Λ(x)=exp(−e
−x
),x∈R
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.
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