• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1537-1545
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• 2015

Support vector quantile regression (SVQR) can be obtained by applying support vector machine with a check function instead of an e-insensitive loss function into the quantile regression, which still requires to solve a quadratic program (QP) problem which is time and memory expensive. In this paper we propose an SVQR whose objective function is composed of an asymmetric quadratic loss function. The proposed method overcomes the weak point of the SVQR with the check function. We use the iterative procedure to solve the objective problem. Furthermore, we introduce the generalized cross validation function to select the hyper-parameters which affect the performance of SVQR. Experimental results are then presented, which illustrate the performance of proposed SVQR.

• Journal of the military operations research society of Korea
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• v.23 no.2
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• pp.135-154
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• 1997

This paper deals with the perishable inventory models with uncertainties of demand functions. The traditional perishable inventory costs of holding and stockout are incorporated into the cost function. The average expected cost will be minimized to find the optimal quantile estimator. After three candidate estimators are proposed on the basis of order statistics, they will be evaluated by the simulation results and statistical analysis. Then the transition procedure algorithm using this estimator will be proposed to make the optimal decision under uncertainty.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.457-465
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• 2011

Sample entropy (Vasicek, 1976) has poor performance, and several nonparametric entropy estimators have been proposed as alternatives. In this paper, we consider a piecewise uniform density function based on quantiles, which enables us to evaluate entropy in each interval, and study the poor performance of the sample entropy in terms of the poor estimation of lower and upper quantiles. Then we propose some improved entropy estimators by simply modifying the quantile estimators, and compare their performances with some existing estimators.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.160-160
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• 2023

Generally, Global Climate Models (GCM) cannot be used directly due to their inherent error arising from over or under-estimation of climate variables compared to the observed data. Several bias correction methods have been devised to solve this problem. Most of the traditional bias correction methods are one dimensional as they bias correct the climate variables separately. One such method is the Quantile Mapping method which builds a transfer function based on the statistical differences between the GCM and observed variables. Laux et al. introduced a copula-based method that bias corrects simulated climate data by employing not one but two different climate variables simultaneously and essentially extends the traditional one dimensional method into two dimensions. but it has some limitations. This study uses objective functions to address specifically, the limitations of Laux's methods on the Quantile Mapping method. The objective functions used were the observed rank correlation function, the observed moment function and the observed likelihood function. To illustrate the performance of this method, it is applied to ten GCMs for 20 stations in South Korea. The marginal distributions used were the Weibull, Gamma, Lognormal, Logistic and the Gumbel distributions. The tested copula family include most Archimedean copula families. Five performance metrics are used to evaluate the efficiency of this method, the Mean Square Error, Root Mean Square Error, Kolmogorov-Smirnov test, Percent Bias, Nash-Sutcliffe Efficiency and the Kullback Leibler Divergence. The results showed a significant improvement of Laux's method especially when maximizing the observed rank correlation function and when maximizing a combination of the observed rank correlation and observed moments functions for all GCMs in the validation period.

• Journal of the Korean Data and Information Science Society
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• v.24 no.2
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• pp.211-222
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• 2013

We consider the problem of nonparametrically estimating the conditional quantile function from censored data and propose new estimators here. They are based on local logistic regression technique of Lee et al. (2006) and "double-kernel" technique of Yu and Jones (1998) respectively, which are modified versions under random censoring. We compare those with two existing estimators based on a local linear fits using the check function approach. The comparison is done by a simulation study.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.533-545
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• 2017

Quantile regression models provide a variety of useful statistical information by estimating the conditional quantile function of the response variable. However, the traditional linear quantile regression model can lead to the distorted and incorrect results when analysing real data having a nonlinear relationship between the explanatory variables and the response variables. Furthermore, as the complexity of the data increases, it is required to analyse multiple response variables simultaneously with more sophisticated interpretations. For such reasons, we propose a multivariate quantile regression tree model. In this paper, a new split variable selection algorithm is suggested for a multivariate regression tree model. This algorithm can select the split variable more accurately than the previous method without significant selection bias. We investigate the performance of our proposed method with both simulation and real data studies.

• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.625-636
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• 2013

In this paper we study four kernel machines for estimating expected shortfall, which are constructed through combinations of support vector quantile regression (SVQR), restricted SVQR (RSVQR), least squares support vector machine (LS-SVM) and support vector expectile regression (SVER). These kernel machines have obvious advantages such that they achieve nonlinear model but they do not require the explicit form of nonlinear mapping function. Moreover they need no assumption about the underlying probability distribution of errors. Through numerical studies on two artificial an two real data sets we show their effectiveness on the estimation performance at various confidence levels.

• Journal of The Korean Society of Agricultural Engineers
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• v.54 no.6
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• pp.133-142
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• 2012

The objective of this study was to correct the bias of the Representative Concentration Pathways (RCP)-based future precipitation data using a quantile mapping method. This method was adopted to correct extreme values because it was designed to adjust simulated data using probability distribution function. The Generalized Extreme Value (GEV) distribution was used to fit distribution for precipitation data obtained from the Korea Meteorological Administration (KMA). The resolutions of precipitation data was 12.5 km in space and 3-hour in time. As the results of bias correction over the past 30 years (1976~2005), the annual precipitation was increased 16.3 % overall. And the results for 90 years (divided into 2011~2040, 2041~2070, 2071~2100) were that the future annual precipitation were increased 8.8 %, 9.6 %, 11.3 % respectively. It also had stronger correction effects on high value than low value. It was concluded that a quantile mapping appeared a good method of correcting extreme value.

• Journal of Korea Water Resources Association
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• v.49 no.7
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• pp.599-606
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• 2016

The objective of this study is to estimate the unregulated flood frequency from Chungju dam to Yangpyung gauging station for the region affected by dams based on the peak discharges simulated by storage function routing model. From the flood frequency analyses, the quantiles for the unregulated flood frequency at 6 sites have similar pattern to each other, and their averaged quantile almost matched to the result from the regional flood frequency analysis. The quantile and annual mean discharge for the unregulated flood frequency for the downstream of Chungju dam show the similar behaviour to those for the upstream area. While the quantile and the annual mean discharge for the regulated flood frequency are significantly different from those for the unregulated flood frequency. In particular, the qunatile shows severe difference as the return period increases, and the annual mean discharge has a tendency to approach to the natural flood as the distance from dam increases.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.87-98
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• 2017

The multivaiate empirical distribution function (MEDF) is defined in this work. The MEDF's expectation and variance are derived and we have shown the MEDF converges to its real distribution function. Based on random samples from bivariate standard normal distribution with various correlation coefficients, we also obtain MEDFs and propose two kinds of graphical methods to visualize MEDFs on two dimensional plane. One is represented with at most n stairs with similar arguments as the step function, and the other is described with at most n curves which look like bivariate quantile vector. Even though these two descriptive methods could be expressed with three dimensional space, two dimensional representation is obtained with ease and it is enough to explain characteristics of bivariate distribution functions. Hence, it is possible to visualize trivariate empirical distribution functions with three dimensional quantile vectors. With bivariate and four variate illustrative examples, the proposed MEDFs descriptive plots are obtained and explored.