Extreme value theory (EVT) provides an elegant mathematical tool for statistical analysis of rare events. Typically, when data are collected from multiple clusters, analysts want to preserve cluster information, such as region, period, and group. To consider large-sized cluster information in extreme value analysis, we incorporate the mixed effects model (MEM) into the regression technique in EVT. In the field of small area estimation, it is well known that the MEM is an important tool for providing reliable estimates of large-sized clusters with small sample sizes. In the context of EVT for rare event analysis, the sample size of extreme value data for each cluster is often small. Therefore, the MEM may contribute to improving the predictive accuracy of extreme value analysis. This motivates us to verify the effectiveness of the MEM in EVT through theoretical studies and numerical experiments, including its application to the risk assessment of heavy rainfall in Japan.

翻译：极值理论为罕见事件的统计分析提供了优雅的数学工具。当数据从多个聚类收集时，分析者通常希望保留聚类信息，如区域、时段和组别。为在极值分析中考虑大规模聚类信息，我们将混合效应模型引入极值理论的回归技术。在小区域估计领域，混合效应模型作为为小样本量的大规模聚类提供可靠估计的重要工具已广为人知。在面向罕见事件分析的极值理论情境下，每个聚类的极值数据样本量往往较小。因此，混合效应模型可能有助于提升极值分析的预测精度。这促使我们通过理论研究与数值实验（包括其在日本强降雨风险评估中的应用）来验证混合效应模型在极值理论中的有效性。