• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.403-412
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• 2004

We obtain a kernel quantile process based on the kernel quantile estimator and prove the uniform consistency of the kernel quantile process by developing that of the usual sample quantile process. We apply our result to the classical kernel type processes.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1539-1547
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• 2014

In this paper we apply the autoregressive process to the nonlinear quantile regression in order to infer nonlinear quantile regression models for the autocorrelated data. We propose a kernel method for the autoregressive data which estimates the nonlinear quantile regression function by kernel machines. Artificial and real examples are provided to indicate the usefulness of the proposed method for the estimation of quantile regression function in the presence of autocorrelation between data.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.733-745
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• 2017

Local composite quantile regression is a useful non-parametric regression method widely used for its high efficiency. Data smoothing methods using kernel are typically used in the estimation process with performances that rely largely on the smoothing parameter rather than the kernel. However, $L_2$-norm is generally used as criterion to estimate the performance of the regression function. In addition, many studies have been conducted on the selection of smoothing parameters that minimize mean square error (MSE) or mean integrated square error (MISE). In this paper, we explored the optimality of selecting smoothing parameters that determine the performance of non-parametric regression models using local linear composite quantile regression. As evaluation criteria for the choice of smoothing parameter, we used mean absolute error (MAE) and mean integrated absolute error (MIAE), which have not been researched extensively due to mathematical difficulties. We proved the uniqueness of the optimal smoothing parameter based on MAE and MIAE. Furthermore, we compared the optimal smoothing parameter based on the proposed criteria (MAE and MIAE) with existing criteria (MSE and MISE). In this process, the properties of the proposed method were investigated through simulation studies in various situations.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.3
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• pp.117-124
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• 2021

The development of IOT technology and artificial intelligence technology is promoting the smartization of manufacturing system. In this study, data extracted from acceleration sensor and current sensor were obtained through experiments in the cutting process of SKD11, which is widely used as a material for special mold steel, and the amount of tool wear and product surface roughness were measured. SVR (Support Vector Regression) is applied to predict the roughness of the product surface in real time using the obtained data. SVR, a machine learning technique, is widely used for linear and non-linear prediction using the concept of kernel. In particular, by applying GSVQR (Generalized Support Vector Quantile Regression), overestimation, underestimation, and neutral estimation of product surface roughness are performed and compared. Furthermore, surface roughness is predicted using the linear kernel and the RBF kernel. In terms of accuracy, the results of the RBF kernel are better than those of the linear kernel. Since it is difficult to predict the amount of tool wear in real time, the product surface roughness is predicted with acceleration and current data excluding the amount of tool wear. In terms of accuracy, the results of excluding the amount of tool wear were not significantly different from those including the amount of tool wear.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.109-120
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• 2002

In this paper, we show the weak convergence of U-empirical processes for two sample problem. We use the result to show the asymptotic normality for the generalized dodges-Lehmann estimates with the Bahadur representation for quantifies of U-empirical distributions. Also we consider the asymptotic normality for the test statistics in a simple way.