• The Korean Journal of Applied Statistics
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• v.33 no.5
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• pp.569-578
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• 2020

By estimating conditional quantile functions of the response, quantile regression (QR) can provide comprehensive information of the relationship between the response and the predictors. In addition, kernel quantile regression (KQR) estimates a nonlinear conditional quantile function in reproducing kernel Hilbert spaces generated by a positive definite kernel function. However, it is infeasible to use the KQR in analysing a massive data due to the limitations of computer primary memory. We propose a divide and conquer based KQR (DC-KQR) method to overcome such a limitation. The proposed DC-KQR divides the entire data into a few subsets, then applies the KQR onto each subsets and derives a final estimator by aggregating all results from subsets. Simulation studies are presented to demonstrate the satisfactory performance of the proposed method.

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.19-27
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• 1998

We considered the bandwidth selection method which has asymptotic optimal convergence rate $n^{-1/2}$ in kernel regression function estimation. For the proposed bandwidth selection, we considered Mean Averaged Squared Error as a performance criterion and its Taylor expansion to the fourth order. Then we estimate the bandwidth which minimizes the estimated approximate value of MASE. Finally we show the relative convergence rate between optimal bandwidth and proposed bandwidth.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2022.06a
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• pp.1350-1352
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• 2022

본 논문에서는 희소깊이영상과 컬러영상을 이용해 조밀한 깊이영상을 추정하는 깊이 완성(depth completion)을 수행하기위해 최근접 이웃 커널을 추정하는 방식의 네트워크를 제안한다. 회귀방식의 딥러닝 네트워크는 일반적으로 값을 직접 예측하는 것보다 기본 값에 더해질 잔차를 추정하는 방식이 더욱 효율적이다. 본 논문에서는 최근접 이웃 커널을 입력영상에 적용하여 추정하고자 하는 픽셀의 인근 픽셀에서 값을 가져와 기본 값으로 사용하고, 해당 값의 잔차를 회귀방식으로 추정하는 네트워크를 설계했다. 이러한 방식으로 여러 SOTA 알고리즘 대비 좋은 성능을 나타냈고, 특히 이와 유사한 방식인 Plane-residual net 보다 높은 성능을 보여준다.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2016.11a
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• pp.85-88
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• 2016

대비 강화는 컴퓨터 비젼, 영상 처리, 패턴인식에서 전처리 과정으로 이용되며 그 역할이 중요하다. 2차원 히스토그램을 이용한 대비 강화 방법은 인접 픽셀 간의 정보를 이용해 대비를 강화시키기 때문에 1차원 히스토그램을 이용한 대비 강화 방법보다 우수하다. 2차원 히스토그램 기반 알고리즘에서 2차원 히스토그램의 인접픽셀 간의 화소값 차이에 따라 가중치를 주는 커널 (kernel)이 사용된다. 이러한 커널은 영상 마다 같은 가중치를 곱해주기 때문에 원하는 대비를 시켜주지 못하는 단점이 있다. 이에 본 논문은 2차원 히스토그램을 1차원 히스토그램으로 정사영을 시켜 평균값과 표준편차를 통해 2차원 히스토그램을 통계학적으로 분석한다. 그리고 선형회귀법을 이용하여 2차원 히스토그램의 통계적 정보에 따른 적응적 가중치 커널을 제안하고, 이를 이용하여 효율적 대비 강화를 한다. 실험 결과를 통해 제안하는 방법이 기존의 알고리즘에 비해 대비 향상 성능이 더 우수한 방법임을 확인하였다.

• Journal of the Korean Data and Information Science Society
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• v.28 no.5
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• pp.971-980
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• 2017

The varying coefficient regression model has gained lots of attention since it is capable to model dynamic changes of regression coefficients in many regression problems of science. In this paper we propose a varying coefficient regression model that effectively considers the errors on both input and response variables, which utilizes the kernel method in estimating the varying coefficient which is the unknown nonlinear function of smoothing variables. We provide a generalized cross validation method for choosing the hyper-parameters which affect the performance of the proposed model. The proposed method is evaluated through numerical studies.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.51-59
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• 2010

In the case that the regression function has a discontinuity point in generalized linear model, Huh (2009) estimated the location and jump size using the log-likelihood weighted the one-sided kernel function. In this paper, we consider estimation of the unknown number of the discontinuity points in the regression function. The proposed algorithm is based on testing of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size described in Huh (2009). The finite sample performance is illustrated by simulated example.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.05a
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• pp.67-68
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• 2010

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.443-444
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• 2011

• 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.