In extreme value analysis, tail behavior of a heavy-tailed data distribution is modeled by a Pareto-type distribution in which the so-called extreme value index (EVI) controls the tail behavior. For heavy-tailed data obtained from multiple population subgroups, or areas, this study efficiently predicts the EVIs of all areas using information among areas. For this purpose, we propose a mixed effects model, which is a useful approach in small area estimation. In this model, we represent differences among areas in the EVIs by latent variables called random effects. Using correlated random effects across areas, we incorporate the relations among areas into the model. The obtained model achieves simultaneous prediction of EVIs of all areas. Herein, we describe parameter estimation and random effect prediction in the model, and clarify theoretical properties of the estimator. Additionally, numerical experiments are presented to demonstrate the effectiveness of the proposed method. As an application of our model, we provide a risk assessment of heavy rainfall in Japan.

翻译：在极值分析中，重尾数据分布的尾部行为通过帕累托型分布建模，其中所谓的极值指数控制尾部行为。对于从多个总体子组（或区域）获得的重尾数据，本研究利用区域间的信息有效预测所有区域的EVI。为此，我们提出了一种混合效应模型，这是小区域估计中的一种有效方法。在该模型中，我们通过称为随机效应的潜变量来表示各区域EVI间的差异。通过使用跨区域相关的随机效应，我们将区域间的关系纳入模型。所得模型实现了对所有区域EVI的同步预测。本文描述了模型中的参数估计与随机效应预测，并阐明了估计量的理论性质。此外，通过数值实验展示了所提方法的有效性。作为模型的应用，我们提供了日本强降雨的风险评估。