arXiv subjects

Koki Momoki

Publications and source records attributed to Koki Momoki.

4 recordsLinked to original sources

arXiv2026

Structural grouping of extreme value models via graph fused lasso

The generalized Pareto distribution (GPD) is a fundamental model for analyzing the tail behavior of a distribution. In particular, the shape parameter of the GPD characterizes the extremal properties of the distribution. As described in this paper, we propose a method for grouping shape parameters in the GPD for clustered data via graph fused lasso. The proposed method simultaneously estimates the model parameters and identifies which clusters can be grouped together. We establish the asymptotic theory of the proposed estimator and demonstrate that its variance is lower than that of the cluster-wise estimator. This variance reduction not only enhances estimation stability but also provides a principled basis for identifying homogeneity and heterogeneity among clusters in terms of their tail behavior. We assess the performance of the proposed estimator through Monte Carlo simulations. As an illustrative example, our method is applied to rainfall data from 996 clustered sites across Japan.

stat.ME↗

arXiv2026

Small area estimation of dependent extreme value indices

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.

stat.ME↗

arXiv2023

Mixed effects models for extreme value index regression

Extreme value theory (EVT) provides an elegant mathematical tool for the statistical analysis of rare events. When data are collected from multiple population subgroups, because some subgroups may have less data available for extreme value analysis, a scientific interest of many researchers would be to improve the estimates obtained directly from each subgroup. 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 producing reliable estimates for subgroups with small sample sizes, i.e., ``small areas.'' The key idea of MEM is to incorporate information from all subgroups into a single model and to borrow strength from all subgroups to improve estimates for each subgroup. Using this property, in extreme value analysis, the MEM may contribute to reducing the bias and variance of the direct estimates from each subgroup. This prompts us to evaluate the effectiveness of the MEM for EVT through theoretical studies and numerical experiments, including its application to the risk assessment of a number of stocks in the cryptocurrency market.

stat.ME↗

arXiv2022

Hypothesis testing for varying coefficient models in tail index regression

This study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact, the varying coefficient model is useful in mean, quantile, and other regressions. The tail index regression is not an exception. However, the varying coefficient model is flexible, but leaner and simpler models are preferred for applications. Therefore, it is important to evaluate whether the estimated coefficient function varies significantly with covariates. If the effect of the non-linearity of the model is weak, the varying coefficient structure is reduced to a simpler model, such as a constant or zero. Accordingly, the hypothesis test for model assessment in the varying coefficient model has been discussed in mean and quantile regression. However, there are no results in tail index regression. In this study, we investigate the asymptotic properties of an estimator and provide a hypothesis testing method for varying coefficient models for tail index regression.

math.ST↗