Small area estimation of dependent extreme value indices

TL;DR

This paper introduces a mixed effects model for small area estimation of extreme value indices in heavy-tailed data, leveraging correlations among areas to improve tail risk predictions, demonstrated through simulations and rainfall risk assessment.

Contribution

It proposes a novel mixed effects model with correlated random effects for joint EVI estimation across multiple areas, enhancing prediction accuracy in extreme value analysis.

Findings

Model effectively predicts EVIs across areas.

Theoretical properties of estimators are established.

Numerical experiments confirm the model's usefulness.

Abstract

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.