• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.408-413
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• 2005

A new methodology for discrete non-Gaussian probability density estimation is investigated in this paper based on a dynamic Bayesian network (DBN) and kernel functions. The estimator consists of a DBN in which the transition distribution is represented with kernel functions. The estimator parameters are determined through a recursive learning algorithm according to the maximum likelihood (ML) scheme. A discrete-type Poisson distribution is generated in a simulation experiment to evaluate the proposed method. In addition, an unknown probability density generated by nonlinear transformation of a Poisson random variable is simulated. Computer simulations numerically demonstrate that the method successfully estimates the unknown probability distribution function (PDF).

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1419-1427
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• 2008

This paper shows the kernel Poisson regression which can be applied in the claims reserving, where the row effect is assumed to be a nonlinear function of the row index. The paper concentrates on the chain-ladder technique, within the framework of the chain-ladder linear model. It is shown that the proposed method can provide better reserve estimates than the Poisson model. The cross validation function is introduced to choose optimal hyper-parameters in the procedure. Experimental results are then presented which indicate the performance of the proposed model.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.109-120
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• 2023

The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗 (Ω) over some set Ω with the reproducing kernel k_λ is defined by $${\tilde{A}}(\lambda)=\,\;{\lambda}{\in}{\Omega}$$. The Berezin number of an operator A is defined by $$ber(A):=\sup_{{\lambda}{\in}{\Omega}}{\mid}{\tilde{A}}({\lambda}){\mid}$$. We study some problems of operator theory by using this bounded function Ã, including estimates for Berezin numbers of some operators, including truncated Toeplitz operators. We also prove an operator analog of some Young inequality and use it in proving of some inequalities for Berezin number of operators including the inequality ber (AB) ≤ ber (A) ber (B), for some operators A and B on 𝓗 (Ω). Moreover, we give in terms of the Berezin number a necessary condition for hyponormality of some operators.

• 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 $C^n$.

• 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 Korea Institute of Military Science and Technology
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• v.23 no.1
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• pp.1-10
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• 2020

Effective jamming in electronic warfare depends on proper jamming technique selection and jamming parameter estimation. For this purpose, this paper proposes a new method of estimating jamming parameters using Gaussian kernel function networks. In the proposed approach, a new method of determining the optimal structure and parameters of Gaussian kernel function networks is proposed. As a result, the proposed approach estimates the jamming parameters in a reliable manner and outperforms other methods such as the DNN(Deep Neural Network) and SVM(Support Vector Machine) estimation models.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.329-368
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• 1999

This paper surveys recent remarkable progress in the study of potential theory for symmetric stable processes. It also contains new results on the two-sided estimates for Green functions Poisson kernels and Martin kernels of discontinuous symmetric $alpha$ -stable process in bounded $C^{1,1}$ open sets. The new results give ex-plicit information on how the comparing constants depend on pa-rametrer $alpha$ and consequently recover the green function and Poisson kernel estimates for Brownian motion by passing $alpha{\uparrow}2$. In addition to these new estimates this paper surveys recent progress in the study of notions of harmonicity integral representation of harmonic func-tions boundary harnack inequality conditional gauge and intrinsic ultracontractivity for symmetric stable processes. Here is a table of contents.

• Journal of Electrical Engineering and Technology
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• v.12 no.4
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• pp.1406-1416
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• 2017

In complex and large-scale industries, properly designed fault detection and identification (FDI) systems considerably improve safety, reliability and availability of target processes. In thermal power plants (TPPs), generating units operate under very dangerous conditions; system failures can cause severe loss of life and property. In this paper, we propose a bagged auto-associative kernel regression (AAKR)-based FDI approach for steam boilers in TPPs. AAKR estimates new query vectors by online local modeling, and is suitable for TPPs operating under various load levels. By combining the bagging method, more stable and reliable estimations can be achieved, since the effects of random fluctuations decrease because of ensemble averaging. To validate performance, the proposed method and comparison methods (i.e., a clustering-based method and principal component analysis) are applied to failure data due to water wall tube leakage gathered from a 250 MW coal-fired TPP. Experimental results show that the proposed method fulfills reasonable false alarm rates and, at the same time, achieves better fault detection performance than the comparison methods. After performing fault detection, contribution analysis is carried out to identify fault variables; this helps operators to confirm the types of faults and efficiently take preventive actions.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.1-28
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• 2014

We consider the hypergeometric translation operator associated to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type $B_2$. We prove in this paper that these operators are positivity preserving and allow positive integral representations. In particular we deduce that the product formulas of the Opdam-Cherednik and the Heckman-Opdam kernels are positive integral transforms, and we obtain best estimates of these kernels. The method used to obtain the previous results shows that these results are also true in the case of the root system of type $C_2$.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.161-172
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• 2005

In this paper a nonparametric method is proposed for detecting conditionally heteroscedastic errors in a nonparametric time series regression model where the observation points are equally spaced on [0,1]. It turns out that the first-order sample autocorrelation of the squared residuals from the kernel regression estimates provides essential information. Illustrative simulation study is presented for diverse errors such as ARCH(1), GARCH(1,1) and threshold-ARCH(1) models.