Estimation of Husler-Reiss distributions and Brown-Resnick processes
Estimation of Husler-Reiss distributions and Brown-Resnick processes
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DOI：
10.1111/rssb.12074
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发表时间：
2015-01-01
影响因子：
5.8
通讯作者：
Schlather, Martin
中科院分区：
文献类型：
--
作者：
Engelke, Sebastian;Malinowski, Alexander;Schlather, Martin
根据多元最大稳定分布的最大吸引域中的观测值估计极值参数通常使用聚集数据，例如块最大值。相比之下，多变量超阈值峰值方法利用来自非聚合的“大”观测的额外信息。我们介绍了一种方法的基础上超过阈值的峰值，提供了几个新的估计过程eta的最大域的吸引力的经常使用的Husler-Reiss模型及其空间扩展：布朗-Resnick过程。该方法依赖于增量eta（.）- 以超过高阈值为条件，其中t（0）是固定位置。当边际被标准化为Gumbel分布时，这些增量渐近地形成高斯过程，从而导致Husler-Reiss参数矩阵的计算简单估计，并且特别地使得基于（高维）多变量密度的Brown-Resnick过程的参数推断成为可能。这是一个主要的优势，在空间极值统计中常用的复合似然方法，因为它们只依赖于双变量密度。仿真研究比较了新的估计与其他常用的方法的性能。作为一个应用程序，我们适合一个非各向同性的布朗-雷斯尼克过程的极端12年的每日风速测量数据。
Estimation of extreme value parameters from observations in the max-domain of attraction of a multivariate max-stable distribution commonly uses aggregated data such as block maxima. Multivariate peaks-over-threshold methods, in contrast, exploit additional information from the non-aggregated 'large' observations. We introduce an approach based on peaks over thresholds that provides several new estimators for processes eta in the max-domain of attraction of the frequently used Husler-Reiss model and its spatial extension: Brown-Resnick processes. The method relies on increments eta(.) - eta t(0)/conditional on eta t(0)/exceeding a high threshold, where t(0) is a fixed location. When the marginals are standardized to the Gumbel distribution, these increments asymptotically form a Gaussian process resulting in computationally simple estimates of the Husler-Reiss parameter matrix and particularly enables parametric inference for Brown-Resnick processes based on (high dimensional) multivariate densities. This is a major advantage over composite likelihood methods that are commonly used in spatial extreme value statistics since they rely only on bivariate densities. A simulation study compares the performance of the new estimators with other commonly used methods. As an application, we fit a non-isotropic Brown-Resnick process to the extremes of 12-year data of daily wind speed measurements.