共查询到20条相似文献,搜索用时 15 毫秒
1.
The extremal coefficients are the natural dependence measures for multivariate extreme value distributions. For an m-variate distribution 2m distinct extremal coefficients of different orders exist; they are closely linked and therefore a complete set of 2m coefficients cannot take any arbitrary values. We give a full characterization of all the sets of extremal coefficients. To this end, we introduce a simple class of extreme value distributions that allows for a 1-1 mapping to the complete sets of extremal coefficients. We construct bounds that higher order extremal coefficients need to satisfy to be consistent with lower order extremal coefficients. These bounds are useful as lower order extremal coefficients are the most easily inferred from data. 相似文献
2.
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
3.
Seokhoon Yun 《Journal of multivariate analysis》1997,63(2):277-295
The paper gives sufficient conditions for domains of attraction of multivariate extreme value distributions. Under the assumption of absolute continuity of a multivariate distribution, the criteria enable one to examine, by using limits of some rescaled conditional densities, whether the distribution belongs to the domain of attraction of some multivariate extreme value distribution. If this is the case, the criteria also determine how to construct such an extreme value distribution. Unlike the criterion given by de Haan and Resnick [1987,Stochastic Process. Appl.2583–93], the criteria are easily applicable even when the marginal tails are not Pareto-like. 相似文献
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5.
A class of multivariate distributions that are mixtures of the positive powers of a max-infinitely divisible distribution are studied. A subclass has the property that all weighted minima or maxima belong to a given location or scale family. By choosing appropriate parametric families for the mixing distribution and the distribution being mixed, families of multivariate copulas with a flexible dependence structure and with closed form cumulative distribution functions are obtained. Some dependence properties of the class, as well as some characterizations, are given. Conditions for max-infinite divisibility of multivariate distributions are obtained. 相似文献
6.
杨旭 《数学的实践与认识》2006,36(12):193-197
针对银行操作风险损失分布的厚尾性和损失事件之间的尾部相依性,首先用单变量极值理论建立了单个损失事件计量模型,然后用多变量极值的连接函数反映了损失事件之间的尾部相依性,避免了计量中对银行操作风险的低估和对监管资本要求高估. 相似文献
7.
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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9.
针对多元函数稳定点处二阶偏导数全为0的情况,提出了有效的极值判别法.定义了广义n维方阵、n次型及其正定性;提出了更具普遍意义的极值充分条件;得到了利用n次型的正定性判断n元函数极值的方法并举例验证了结论的正确性和有效性. 相似文献
10.
本文对二元函数极值的充分条件作了进一步的讨论 ,得到了 AC-B2 =0时 ,二元函数极值判定的充分条件 相似文献
11.
给出了 n元函数极值的一个充分条件 ,并结合矩阵的初等变换建立了 n元函数极值的一种快速判别法 ,最后给出了一个例子 相似文献
12.
A test statistic is developed that checks the validity of the extreme value conditions without specifiying the shape parameter of the limiting extreme value distribution. 相似文献
13.
For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results are established for thed-dimensional renewal process. Similar theorems for the estimated version of this process are also derived. These results are suggested to serve as simultaneous asymptotic testing devices for detecting changes in the multivariate setting. 相似文献
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Dependence Measures for Extreme Value Analyses 总被引:16,自引:0,他引:16
Quantifying dependence is a central theme in probabilistic and statistical methods for multivariate extreme values. Two situations are possible: one where, in a limiting sense, the extremes are dependent; the other where, in the same sense, the extremes are independent. This paper comprises an overview of the principal issues through a unified approach which encompasses both these situations. Novel diagnostic measures for dependence are also developed which provide complementary information about different aspects of extremal dependence. The paper is written in an elementary style, with the methodology illustrated by application to theoretical examples and typical data-sets. These data-sets and the S-plus functions used for the analyses are available online. 相似文献
16.
史道济 《应用数学学报(英文版)》1995,11(4):421-428
MULTIVARIATEEXTREMEVALUEDISTRIBUTIONANDITSFISHERINFORMATIONMATRIX¥SHIDAOJI(史道济)(DepartmentofMathematics,TianjinUniversity,Tia... 相似文献
17.
Frank Marohn 《Extremes》2000,3(4):363-384
We consider the full statistical families of extreme value distributions
and generalized Pareto distributions
, where
, and
denote the shape, scale and location parameters, respectively. We consider the testing problems
against
and = 0 against 0, where and are treated as nuisance parameters. Showing local asymptotic normality (LAN), we derive asymptotic envelope power functions for test sequences and establish tests which attain these upper bounds. The finite sample size behavior is studied by simulations. 相似文献
18.
Effects of Mis-Specification in Bivariate Extreme Value Problems 总被引:3,自引:0,他引:3
The need to incorporate the structure of complex problems in extreme value analyzes, and the requirement to exploit all the limited information that is available, has led to the increased use of advanced dependence models. When they are appropriate, these dependence models can lead to substantial benefits over simpler univariate extreme value methods. Here we explore some inference problems for the marginal and conditional distributions caused by model mis-specification. We find distinct differences in estimation characteristics when the dependence structure is asymptotically dependent or asymptotically independent, and that conditional models can be substantially improved if the variables are standardized to have common marginal distributions. 相似文献
19.
Likelihood-Based Inference for Extreme Value Models 总被引:7,自引:0,他引:7
Estimation of the extremal behavior of a process is often based on the fitting of asymptotic extreme value models to relatively short series of data. Maximum likelihood has emerged as a flexible and powerful modeling tool in such applications, but its performance with small samples has been shown to be poor relative to an alternative fitting procedure based on probability weighted moments. We argue here that the small-sample superiority of the probability weighted moments estimator is due to the assumption of a restricted parameter space, corresponding to finite population moments. To incorporate similar information in a likelihood-based analysis, we propose a penalized maximum likelihood estimator that retains the modeling flexibility and large-sample optimality of the maximum likelihood estimator, but improves on its small-sample properties. The properties of the penalized likelihood estimator are verified in a simulation study, and in application to sea-level data, which also enables the procedure to be evaluated in the context of structural models for extremes. 相似文献