随机场两个区域上极大值的广义madogram和两两相依性

Non-parametric estimator of a multivariate madogram for missing-data and extreme value framework

The modeling of dependence between maxima is an important subject in several applications in risk analysis. To this aim, the extreme value copula function, characterised via the madogram, can be used as a margin-free description of the dependence structure. From a practical point of view, the family of extreme value distributions is very rich and arise naturally as the limiting distribution of properly normalised component-wise maxima. In this paper, we investigate the nonparametric estimation of the madogram where data are completely missing at random. We provide the functional central limit …

Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials

Many applications in risk analysis, especially in environmental sciences, require the estimation of the dependence among multivariate maxima. A way to do this is by inferring the Pickands dependence function of the underlying extreme-value copula. A nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of a specific type of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-s…

通过自助法最大化U-统计量检验高维数据中具有实际显著性的依赖关系

Testing for practically significant dependencies in high dimensions via bootstrapping maxima of U-statistics

本文研究高维向量分量独立性检验，将原假设设为所有两两关联绝对值不超过某阈值，针对可由U-统计量估计的依赖性度量，提出了渐近和自助法水平α检验，并证明其minimax最优性。

Penalized linear regression with high-dimensional pairwise screening

In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and penalization. We achieve this by studying the asymptotic distribution of the maximal absolute pairwise sample correlation among independent covariates. The novelty of the theory is in that the convergence is with respect to the dimensionality $p$, and is uniform with respect to the sample size $n$. Moreover, we obtain an upper bound for the maximal pairwise R squared wh…

A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes

In modeling spatial extremes, the dependence structure is classically inferred by assuming that block maxima derive from max-stable processes. Weather stations provide daily records rather than just block maxima. The point process approach for univariate extreme value analysis, which uses more historical data and is preferred by some practitioners, does not adapt easily to the spatial setting. We propose a two-step approach with a composite likelihood that utilizes site-wise daily records in addition to block maxima. The procedure separates the estimation of marginal parameters and dependence …

极端事件的时空模拟

Space-time modelling of extreme events

最大稳定过程是模拟空间和时间极端事件的广义极值分布的自然类似物。在适当的条件下，这些过程是随机场的独立重复的最大值的渐近合理模型，它们也适合于高阈值上联合个体极值测量的建模。本文将Schlather（2001）的一个模型推广到空时框架，并证明了在轻度混合条件下，如何利用成对截尾似然估计进行相合估计。估计效率也进行了评估，并讨论了简单的时间序列模型计算的基础上的成对似然对的选择。的想法说明了瑞士每小时的降水数据的应用程序。