arXiv subjects

Yire Shin

Publications and source records attributed to Yire Shin.

6 recordsLinked to original sources

arXiv2026

Automated selection of r for stationary and nonstationary models for r largest order statistics

In generalized extreme value model for the r largest order statistics, denoted by rGEV, the selection of r is critical. The existing entropy difference test for selecting r is applicable to large sample. Another existing method (the score test with parametric bootstrap) is applicable to small sample, but computationally demanding. To address this problem for small sample, we propose a new method using a sequence of the goodness-of-fit tests based on the conditional cumulative distribution function (CCDF). The proposed CCDF test is easy to implement and computationally fast. The Cram{\'e}r-von Mises test was employed for the goodness-of-fit purpose. The proposed method is compared via Monte Carlo simulations with existing methods including the spacings, the score, and the entropy difference tests. The proposed CCDF test turned out to perform well for both small and large samples, comparable to the spacings and entropy difference tests. The utility of the proposed method is illustrated by an application to the r largest daily rainfall data in Korea. Additionally, we extended the existing methods and the CCDF test to a nonstationary rGEV model. Wide applicability of the proposed method are discussed.

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arXiv2025

Generalized method of L-moment estimation for stationary and nonstationary extreme value models

Precisely estimating out-of-sample upper quantiles is very important in risk assessment and in engineering practice for structural design to prevent a greater disaster. For this purpose, the generalized extreme value (GEV) distribution has been broadly used. To estimate the parameters of GEV distribution, the maximum likelihood estimation (MLE) and L-moment estimation (LME) methods have been primarily employed. For a better estimation using the MLE, several studies considered the generalized MLE (penalized likelihood or Bayesian) methods to cooperate with a penalty function or prior information for parameters. However, a generalized LME method for the same purpose has not been developed yet in the literature. We thus propose the generalized method of L-moment estimation (GLME) to cooperate with a penalty function or prior information. The proposed estimation is based on the generalized L-moment distance and a multivariate normal likelihood approximation. Because the L-moment estimator is more efficient and robust for small samples than the MLE, we reasonably expect the advantages of LME to continue to hold for GLME. The proposed method is applied to the stationary and nonstationary GEV models with two novel (data-adaptive) penalty functions to correct the bias of LME. A simulation study indicates that the biases of LME are considerably corrected by the GLME with slight increases in the standard error. Applications to US flood damage data and maximum rainfall at Phliu Agromet in Thailand illustrate the usefulness of the proposed method. This study may promote further work on penalized or Bayesian inferences based on L-moments.

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arXiv2025

Building nonstationary extreme value model using L-moments

The maximum likelihood estimation for a time-dependent nonstationary (NS) extreme value model is often too sensitive to influential observations, such as large values toward the end of a sample. Thus, alternative methods using L-moments have been developed in NS models to address this problem while retaining the advantages of the stationary L-moment method. However, one method using L-moments displays inferior performance compared to stationary estimation when the data exhibit a positive trend in variance. To address this problem, we propose a new algorithm for efficiently estimating the NS parameters. The proposed method combines L-moments and robust regression, using standardized residuals. A simulation study demonstrates that the proposed method overcomes the mentioned problem. The comparison is conducted using conventional and redefined return level estimates. An application to peak streamflow data in Trehafod in the UK illustrates the usefulness of the proposed method. Additionally, we extend the proposed method to a NS extreme value model in which physical covariates are employed as predictors. Furthermore, we consider a model selection criterion based on the cross-validated generalized L-moment distance as an alternative to the likelihood-based criteria.

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arXiv2025

Model averaging with mixed criteria for estimating high quantiles of extreme values: Application to heavy rainfall

Accurately estimating high quantiles beyond the largest observed value is crucial for risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for this purpose, with L-moment estimation (LME) and maximum likelihood estimation (MLE) being the primary methods. However, estimating high quantiles with a small sample size becomes challenging when the upper endpoint is unbounded, or equivalently, when there are larger uncertainties involved in extrapolation. This study introduces an improved approach using a model averaging (MA) technique. The proposed method combines MLE and LME to construct candidate submodels and assign weights effectively. The properties of the proposed approach are evaluated through Monte Carlo simulations and an application to maximum daily rainfall data in Korea. In addition, theoretical properties of the MA estimator are examined, including the asymptotic variance with random weights. A surrogate model of MA estimation is also developed and applied for further analysis. Finally, a Bayesian model averaging approach is considered to reduce the estimation bias occurring in the MA methods.

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arXiv2024

Generalized logistic model for $r$ largest order statistics, with hydrological application

The effective use of available information in extreme value analysis is critical because extreme values are scarce. Thus, using the $r$ largest order statistics (rLOS) instead of the block maxima is encouraged. Based on the four-parameter kappa model for the rLOS (rK4D), we introduce a new distribution for the rLOS as a special case of the rK4D. That is the generalized logistic model for rLOS (rGLO). This distribution can be useful when the generalized extreme value model for rLOS is no longer efficient to capture the variability of extreme values. Moreover, the rGLO enriches a pool of candidate distributions to determine the best model to yield accurate and robust quantile estimates. We derive a joint probability density function, the marginal and conditional distribution functions of new model. The maximum likelihood estimation, delta method, profile likelihood, order selection by the entropy difference test, cross-validated likelihood criteria, and model averaging were considered for inferences. The usefulness and practical effectiveness of the rGLO are illustrated by the Monte Carlo simulation and an application to extreme streamflow data in Bevern Stream, UK.

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arXiv2020

Modeling climate extremes using the four-parameter kappa distribution for $r$-largest order statistics

Accurate estimation of the T-year return levels of climate extremes using statistical distribution is a critical step in the projection of future climate and in engineering design for disaster response. We show how the estimation of such quantities can be improved by fitting {the four-parameter kappa distribution for $r$-largest order statistics} (rK4D), which was developed in this study. The rK4D is an extension of {the generalized extreme value distribution for $r$-largest order statistics} (rGEVD), similar to the four-parameter kappa distribution (K4D), which is an extension of the generalized extreme value distribution (GEVD). This new distribution (rK4D) can be useful not only for fitting data when three parameters in the GEVD are not sufficient to capture the variability of the extreme observations, but also in reducing the estimation uncertainty by making use of the r-largest extreme observations instead of only the block maxima. We derive a joint probability density function (PDF) of rK4D and the marginal and conditional cumulative distribution functions and PDFs. To estimate the parameters, the maximum likelihood estimation and the maximum penalized likelihood estimation methods were considered. The usefulness and practical effectiveness of the rK4D are illustrated by the Monte Carlo simulation and by an application to the Bangkok extreme rainfall data. A few new distributions for $r$-largest order statistics are also derived as special cases of the rK4D, such as the $r$-largest logistic, the $r$-largest generalized logistic, and the $r$-largest generalized Gumbel distributions. These distributions for $r$-largest order statistics would be useful in modeling extreme values for many research areas, including hydrology and climatology.

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