• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.773-786
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• 2016

Multiple quantile regression that simultaneously estimate several conditional quantiles of response given covariates can provide a comprehensive information about the relationship between the response and covariates. Some quantile estimates can cross if conditional quantiles are separately estimated; however, this violates the definition of the quantile. To tackle this issue, multiple quantile regression with non-crossing constraints have been developed. In this paper, we carry out a comparison study on several popular methods for non-crossing multiple linear quantile regression to provide practical guidance on its application.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1319-1325
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• 2010

Quantile regression provides a more complete statistical analysis of the stochastic relationships among random variables. Sometimes quantile functions estimated at different orders can cross each other. We propose a new non-crossing quantile regression method applying support vector median regression to restricted regression quantile, restricted support vector quantile regression. The proposed method provides a satisfying solution to estimating non-crossing quantile functions when multiple quantiles for high dimensional data are needed. We also present the model selection method that employs cross validation techniques for choosing the parameters which aect the performance of the proposed method. One real example and a simulated example are provided to show the usefulness of the proposed method.

• The Korean Journal of Applied Statistics
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• v.26 no.6
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• pp.915-922
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• 2013

Quantile regression can estimate multiple conditional quantile functions of the response, and as a result, it provide comprehensive information of the relationship between the response and the predictors. However, when estimating several conditional quantile functions separately, two or more estimated quantile functions may cross or overlap and consequently violate the basic properties of quantiles. In this paper, we propose a new stepwise method to estimate multiple non-crossing quantile functions using constraints on the kernel coefficients. A simulation study are presented to demonstrate satisfactory performance of the proposed method.

• The Korean Journal of Applied Statistics
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• v.33 no.6
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• pp.753-762
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• 2020

With an increasing interest in integrating artificial intelligence (AI) into interview processes, the Republic of Korea (ROK) army is trying to lead and analyze AI-powered interview platform. This study is to analyze the AI interview data using a unified non-crossing multiple quantile tree (UNQRT) model. Compared to the UNQRT, the existing models, such as quantile regression and quantile regression tree model (QRT), are inadequate for the analysis of AI interview data. Specially, the linearity assumption of the quantile regression is overly strong for the aforementioned application. While the QRT model seems to be applicable by relaxing the linearity assumption, it suffers from crossing problems among estimated quantile functions and leads to an uninterpretable model. The UNQRT circumvents the crossing problem of quantile functions by simultaneously estimating multiple quantile functions with a non-crossing constraint and is robust from extreme quantiles. Furthermore, the single tree construction from the UNQRT leads to an interpretable model compared to the QRT model. In this study, by using the UNQRT, we explored the relationship between the results of the Army AI interview system and the existing personnel data to derive meaningful results.

• Communications for Statistical Applications and Methods
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• v.31 no.6
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• pp.627-644
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• 2024

Quantile regression models have become popular due to their benefits in obtaining robust estimates. Some machine learning (ML) models can estimate conditional quantiles. However, current ML methods mainly focus on just adapting quantile regression. In this paper, we propose a local quantile ensemble based on ML methods, which averages multiple estimated quantiles near the target quantile. It is designed to enhance the stability and accuracy of the quantile fits. This approach extends the composite quantile regression algorithm that typically considers the central tendency under a linear model. The proposed methods can be applied to various types of data having nonlinear and heterogeneous trend. We provide an empirical rule for choosing quantiles around the target quantile. The bias-variance tradeoff inherent in this method offers performance benefits. Through empirical studies using Monte Carlo simulations and real data sets, we demonstrate that the proposed method can significantly improve quantile estimation accuracy and stabilize the quantile fits.

• Journal of Coastal Disaster Prevention
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• v.4 no.3
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• pp.119-131
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• 2017

Global warming under the influence of climate change and its direct impact on glacial and sea level are known issue. However, there is a lack of research on an indirect impact of climate change such as coastal structure design which is mainly based on a frequency analysis of water level under the stationary assumption, meaning that maximum sea level will not vary significantly over time. In general, stationary assumption does not hold and may not be valid under a changing climate. Therefore, this study aims to develop a novel approach to explore possible distributional changes in annual maximum sea levels (AMSLs) and provide the estimate of design water level for coastal structures using a multiple non-crossing quantile regression based nonstationary frequency analysis within a Bayesian framework. In this study, 20 tide gauge stations, where more than 30 years of hourly records are available, are considered. First, the possible distributional changes in the AMSLs are explored, focusing on the change in the scale and location parameter of the probability distributions. The most of the AMSLs are found to be upward-convergent/divergent pattern in the distribution, and the significance test on distributional changes is then performed. In this study, we confirm that a stationary assumption under the current climate characteristic may lead to underestimation of the design sea level, which results in increase in the failure risk in coastal structures. A detailed discussion on the role of the distribution changes for design water level is provided.