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多变量极值的条件方法（附讨论）AI 解读

Summary Multivariate extreme value theory and methods concern the characterization, estimation and extrapolation of the joint tail of the distribution of a d-dimensional random variable. Existing approaches are based on limiting arguments in which all components of the variable become large at the same rate. This limit approach is inappropriate when the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the…

时间序列极端值相依性的诊断AI 解读

Summary The analysis of extreme values within a stationary time series entails various assumptions concerning its long- and short-range dependence. We present a range of new diagnostic tools for assessing whether these assumptions are appropriate and for identifying structure within extreme events. These tools are based on tail characteristics of joint survivor functions but can be implemented by using existing estimation methods for extremes of univariate independent and…

不同采样频率下过程的极值分析AI 解读

Summary The observed extremes of a discrete time process depend on the process itself and the sampling frequency. We develop theoretical results which show how to account for the effect of sampling frequency on extreme values, thus enabling us to analyse systematically extremal data from series with different sampling rates. We present statistical methodology based on these results which we illustrate though simulations and by applications to sea-waves and rainfall data.

联合尾部区域内的依赖建模AI 解读

Summary Standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max-stability, a particular form of joint tail dependence. We develop joint tail models based on a broader class of dependence structure which provides a natural link between max-stable models and weaker forms of dependence including independence and negative association. This approach overcomes many of the problems that are encountered with standard…

多元极值分布建模AI 解读

Multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima/minima. No parametric family exists for the dependence between the margins. This paper extends to more than two variables the models and results for the bivariate case obtained by Tawn (1988). Two new families of physically motivated parametric models for the dependence structure are presented and are illustrated with an application to trivariate extreme sea…

多元极值分布的建模AI 解读

Multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima/minima. No parametric family exists for the dependence between the margins. This paper extends to more than two variables the models and results for the bivariate case obtained by Tawn (1988). Two new families of physically motivated parametric models for the dependence structure are presented and are illustrated with an application to trivariate extreme sea…

二元极值理论：模型与估计AI 解读

Bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima. No natural parametric family exists for the dependence between the marginal distributions, but there are considerable restrictions on the dependence structure. We consider modelling the dependence function with parametric models, for which two new models are presented. Tests for independence, and discriminating between models, are also given. The estimation…