• The Korean Journal of Applied Statistics
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• v.25 no.2
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• pp.341-350
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• 2012

Composite quantile regression model is considered for iid error case. Since the regression coefficients are the same across different quantiles, composite quantile regression can be used to combine the strength across multiple quantile regression models. For the composite quantile regression, bootstrap method is examined for statistical inference including the selection of the number of quantiles and confidence intervals for the regression coefficients. Feasibility of the bootstrap method is demonstrated through a simulation study.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1093-1101
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• 2009

Quantile regression has become a more widely used technique to describe the distribution of a response variable given a set of explanatory variables. This paper proposes a novel modelfor quantile regression using doubly penalized kernel machine with support vector machine iteratively reweighted least squares (SVM-IRWLS). To make inference about the shape of a population distribution, the widely popularregression, would be inadequate, if the distribution is not approximately Gaussian. We present a likelihood-based approach to the estimation of the regression quantiles that uses the asymmetric Laplace density.

• 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.

• 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.29 no.6
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• pp.1095-1106
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• 2016

The quantile regression method proposed by Koenker et al. (1978) focuses on conditional quantiles given by independent variables, and analyzes the relationship between response variable and independent variables at the given quantile. Considering the linear programming used for the estimation of quantile regression coefficients, the model fitting job might be difficult when large data are introduced for analysis. Therefore, dimension reduction (or variable selection) could be a good solution for the quantile regression of large data sets. Regression tree methods are applied to a variable selection for quantile regression in this paper. Real data of Korea Baseball Organization (KBO) players are analyzed following the variable selection approach based on the regression tree. Analysis result shows that a few important variables are selected, which are also meaningful for the given quantiles of salary data of the baseball players.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.707-716
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• 2011

Quantiles and quantile ranks(or plotting positions) are widely used in academia and industry. Sample quantile methods and sample quantile methods implemented in some major statistical software are at least seven, respectively. Small looking differences between the methods can make big differences in outcomes that result from decisions based on them. We discussed the characteristics and differences of the basic plotting position using the empirical cumulative probability and the six plotting positions derived from the suggestion of Blom (1958). After discussing the characteristics and differences of seven quantile methods used in the some major statistical software, we suggested a general expression covering all seven quantile methods. Using the insight obtained from the general expression, we proposed four propositions that make it possible to find the plotting position method that correspond to each of the seven quantile methods. These correspondences may help us to understand and apply quantile methodology.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.147-154
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• 2005

본 논문에서는 집단화된 자료의 분위수들을 계산하는 수정된 방법을 제시하였다. 제시된 방법은 각 계급구간 안의 자료들이 그 구간에 걸쳐 균등한 간격으로, 그리고 구간의 중간점에 관하여 대칭으로 분포하고 있다고 가정하고 분위수들을 계산하는 방법이다. 개개의 자료값들이 주어진 자료를 통하여, 제시된 방법과 기존의 방법을 비교하였다.

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.285-293
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• 2010

The traditional methods for evaluating response surface designs are alphabetic optimality criteria. These single-number criteria such as D-, A-, G- and V-optimality do not completely reflect the prediction variance characteristics of the design in question. Alternatives to single-numbers summaries include graphical displays of the prediction variance across the design regions. We can suggest the animated quantile plots as the animation of the quantile plots and use these animated quantile plots for comparing and evaluating response surface designs.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.749-756
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• 2012

An approach widely used for small area estimation is based on linear mixed models. However, when the functional form of the relationship between the response and the input variables is not linear, it may lead to biased estimators of the small area parameters. In this paper we propose M-quantile kernel regression for small area mean estimation allowing nonlinearities in the relationship between the response and the input variables. Numerical studies are presented that show the sample properties of the proposed estimation method.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1361-1371
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• 2016

Quantile regression provides a variety of useful statistical information to examine how covariates influence the conditional quantile functions of a response variable. However, traditional quantile regression (which assume a linear model) is not appropriate when the relationship between the response and the covariates is a nonlinear. It is also necessary to conduct variable selection for high dimensional data or strongly correlated covariates. In this paper, we propose a penalized quantile regression tree model. The split rule of the proposed method is based on residual analysis, which has a negligible bias to select a split variable and reasonable computational cost. A simulation study and real data analysis are presented to demonstrate the satisfactory performance and usefulness of the proposed method.