• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.149-158
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• 1994

Nonparametric regression technique using kernel estimator is an attractive alternative that has received some attention, recently. The kernel estimate depends on two quantities which have to be provided by the user : the kernel function and the bandwidth. However, the more difficult problem is how to find an appropriate bandwidth which controls the amount of smoothing (see Silverman, 1986). Thus, in practical situation, it is certainly desirable to determine an appropriate bandwidth in some automatic fashion. Thus, the problem is to find a data-driven or adaptive (i.e., depending only on the data and then directly computable in practice) bandwidth that performs reasonably well relative to the best theoretical bandwidth. In this paper, we introduce a relation between bias and variance of mean square error. Thus, we present a simple and effective algorithm for selecting local bandwidths in kernel regression.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1081-1098
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• 2006

Mathematical analysis is made on a mesh free method for the compressible Euler equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed for space approximation. With the backward-Euler method used for time discretization, existence of discrete solution and it's $L^2-error$ estimate are obtained under a regularity assumption of the continuous solution. The result of numerical experiment made on the biconvex airfoil is presented.

• Journal of Korean Society for Quality Management
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• v.25 no.4
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• pp.106-114
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• 1997

The smoothing parameter or bandwidth is crucial to performance of the kernel based regression estimator. So the choice of a "optimal" smoothing parameter produce a single curve estimate. If a single estimate is replaced by a family of estimates, it become easy that we understand what varies with choice of the smoothing parameter. This paper suggests the threshold of the maximum bandwidth and the number of the family members in the regression context.n context.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.661-678
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• 1995

In this paper we will estimate from above and below the values of the Bergman, Caratheodory and Kobayashi metrics for a vector X at z, where z is any point near a given point $z_0$ in the boundary of pseudoconvex domains in $C^n$.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.703-725
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• 2011

In this paper, we establish the vector-valued inequalities for the commutators of singular integrals with rough kernels. In particular, our results can essentially improve some well-known results.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.161-166
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• 2018

This paper deals an impulsive fractional integral inequality with singular kernel which can be used in getting the explicit estimate of solutions of impulsive fractional differential equations.

• Journal of Korean Society for Quality Management
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• v.18 no.2
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• pp.127-133
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• 1990

In this article, several problems inherent in histogram estimate of unknown probability density function are discussed. Those include so called sharp comers and bin edge effect. A resolution for these problems occurred with histogram is discussed. The resulting estimate is called kernel density estimate which is most widely used by data analysts. One of the most recent and reliable data-based choices of scale factor (bandwidth) of the estimate, which has been known to be most crucial, is also discussed.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1045-1054
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• 2012

Support vector machine is known to be the very useful statistical method in classification and nonlinear function estimation. In this paper we propose a monotone support vector regression (SVR) for the estimation of monotonically decreasing function. The proposed monotone SVR is applied to smooth the Kaplan-Meier estimate of survival function. Experimental results are then presented which indicate the performance of the proposed monotone SVR using survival functions obtained by exponential distribution.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.283-287
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• 2010

Stochastic simulation of hydrologic data has been widely developed for several decades. However, despite the several advances made in literature still a number of limitations and problems remain. In the current study, some stochastic simulation approaches tackling some of the existing problems are discussed. The presented models are based on nonparametric techniques such as block bootstrapping, and K-nearest neighbor resampling (KNNR), and kernel density estimate (KDE). Three different types of the presented stochastic simulation models are (1) Pilot Gamma Kernel estimate with KNNR (a single site case) and (2) Enhanced Nonparametric Disaggregation with Genetic Algorithm (a disaggregation case). We applied these models to one of the most challenging and critical river basins in USA, the Colorado River. These models are embedded into the hydrological software package, Pros and cons of the models compared with existing models are presented through basic statistics and drought and storage-related statistics.

• Nuclear Engineering and Technology
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• v.50 no.5
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• pp.673-682
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• 2018

One of the most widely used methods to estimate core damage during a nuclear power plant accident is containment radiation measurement. The evolution of severe accidents is extremely complex, leading to uncertainty in the containment dose rate (CDR). Therefore, it is difficult to accurately determine core damage. This study proposes to conduct uncertainty analysis of CDR for core damage assessment. First, based on source term estimation, the Monte Carlo (MC) and point-kernel integration methods were used to estimate the probability density function of the CDR under different extents of core damage in accident scenarios with late containment failure. Second, the results were verified by comparing the results of both methods. The point-kernel integration method results were more dispersed than the MC results, and the MC method was used for both quantitative and qualitative analyses. Quantitative analysis indicated a linear relationship, rather than the expected proportional relationship, between the CDR and core damage fraction. The CDR distribution obeyed a logarithmic normal distribution in accidents with a small break in containment, but not in accidents with a large break in containment. A possible application of our analysis is a real-time core damage estimation program based on the CDR.