Mixed effects models for large sized clustered extremes
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Extreme value theory (EVT) provides an elegant mathematical tool for the statistical analysis of rare events. Typically, when data consists of multiple clusters, analysts want to preserve cluster information such as region, period, and group. To take into account the large sized cluster information in extreme value analysis, we incorporate the mixed effects model (MEM) into the regression technique in EVT instead of the traditional approach such as multivariate extreme value distribution. The MEM has been recognized not only as a model for clustered data, but also as a tool for providing reliable estimates of large sized clusters with small sample sizes. In EVT for rare event analysis, the effective sample size for each cluster is often small. Therefore, the MEM may also contribute to improving the predictive accuracy of extreme value analysis. However, to the best of our knowledge, the MEM has not yet been developed in the context of EVT. This motivates us to verify the effectiveness of the MEM in EVT through theoretical studies and numerical experiments, including application to real data for risk assessment of heavy rainfall in Japan.
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