The block maxima approach is an important method in univariate extreme value analysis. While assuming that block maxima are independent results in straightforward analysis, the resulting inferences maybe invalid when a series of block maxima exhibits dependence. We propose a model, based on a first-order Markov assumption, that incorporates dependence between successive block maxima through the use of a bivariate logistic dependence structure while maintaining generalized extreme value (GEV) marginal distributions. Modeling dependence in this manner allows us to better estimate extreme quantiles when block maxima exhibit short-ranged dependence. We demonstrate via a simulation study that our first-order Markov GEV model performs well when successive block maxima are dependent, while still being reasonably robust when maxima are independent. We apply our method to two polar annual minimum air temperature data sets that exhibit short-ranged dependence structures, and find that the proposed model yields modified estimates of high quantiles.

中文翻译：

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应用极地温度数据对块极值的短程相关性进行建模

块极大值法是单变量极值分析中的一种重要方法。虽然在简单的分析中假设块最大值是独立的，但当一系列块最大值表现出依赖性时，由此产生的推论可能无效。我们提出了一个基于一阶马尔可夫假设的模型，该模型通过使用双变量逻辑依赖结构合并了连续块最大值之间的依赖关系，同时保持广义极值 (GEV) 边际分布。当块最大值表现出短程依赖性时，以这种方式建模依赖性使我们能够更好地估计极端分位数。我们通过模拟研究证明，我们的一阶马尔可夫 GEV 模型在连续块最大值相关时表现良好，而当最大值独立时仍然相当稳健。