  Extreme value theory (EVT) provides an elegant mathematical tool for
statistically analyzing rare events. When data are collected from multiple
population subgroups, the scientific interest of researchers would generally be
to improve the estimates obtained directly from each subgroup because some
subgroups may have less data available for extreme value analysis. To achieve
this, we incorporate the mixed effects model (MEM) into the regression
technique in EVT. In small area estimation, the MEM has attracted considerable
attention as a primary tool for providing reliable estimates for subgroups with
small sample sizes, that is, ``small area.'' The key idea of the MEM is to
incorporate information from all subgroups into a single model and to borrow
strength from other subgroups to improve estimates by subgroup. Using this
property, the MEM may contribute to reducing the bias and variance of the
direct estimates for each subgroup, which result from the asymptotic
specification of EVT. This prompts us to evaluate MEM's effectiveness in EVT
through theoretical studies and numerical experiments, including its
application to assessing the risk of heavy rainfall in Japan.
