• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.879-895
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• 2022

This paper establishes the Baum-Katz type theorem and the Marcinkiewicz-Zymund type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors {X, X_n, n ≥ 1} taking values in a Hilbert space H with general normalizing constants $b_n=n^{\alpha}{\tilde{L}}(n^{\alpha})$, where ${\tilde{L}}({\cdot})$ is the de Bruijn conjugate of a slowly varying function L(·). The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.531-538
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• 2016

In this paper we deal with the small area estimation for the case that the response variables take binary values. The mixed effects models have been extensively studied for the small area estimation, which treats the spatial effects as random effects. However, when the spatial information of each area is given specifically as coordinates it is popular to use the geographically weighted logistic regression to incorporate the spatial information by assuming that the regression parameters vary spatially across areas. In this paper, relaxing the linearity assumption and propose a geographically weighted kernel logistic regression for estimating small area proportions by using basic principle of kernel machine. Numerical studies have been carried out to compare the performance of proposed method with other methods in estimating small area proportion.

• Journal of Korea Multimedia Society
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• v.7 no.12
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• pp.1639-1649
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• 2004

In this paper, a method for detection of forged signatures based on spectral analysis of directional gradient density function and a weighted fuzzy classifier is proposed. The well defined outline of an incoming signature image is extracted in a preprocessing stage which includes noise reduction, automatic thresholding, image restoration and erosion process. The directional gradient density function derived from extracted signature outline is highly related to the overall shape of signature image, and thus its frequency spectrum is used as a feature set. With this spectral feature set, having a property to be invariant in size, shift, and rotation, a weighted fuzzy classifier is evaluated for the verification of freehand and random forgeries. Experiments show that less than 5% averaged error rate can be achieved on a database of 500 signature samples.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.369-376
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• 2002

The stochastic analysis of semi-infinite domain is presented using the weighted integral method, which is improved to include the higher order terms in expanding the displacement vector. To improve the weighted integral method, the Lagrangian remainder is taken into account in the expansion of the status variable with respect to the mean value of the random variables. In the resulting formulae only the 'proportionality coefficients' are introduced in the resulting equation, therefore no additional computation time and memory requirement is needed. The equations are applied in analyzing the semi-infinite domain. The results obtained by the improved weighted integral method are reasonable and are in good agreement with those of the Monte Carlo simulation. To model the semi-infinite domain, the Bettess's infinite element is adopted, where the theoretical decomposition of the strain-displacement matrix to calculate the deviatoric stiffness of the semi-infinite domains is introduced. The calculated value of mean and the covariance of the displacement are revealed to be larger than those given by the finite domain assumptions which is thought to be rational and should be considered in the design of structures on semi-infinite domains.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.3
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• pp.598-604
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• 2012

Image signal is corrupted by various noises in image processing, many studies are being accomplished to restore those images. In this paper, we proposed a cascade filter algorithm for removing random valued impulse noise. The algorithm consists two steps that noise detection and noise elimination. Variance of filtering mask and center pixel variance are calculated for noise detection, and the noise pixel is replaced by estimated value which first apply switching self adaptive weighted median filter and finally processed by modified weight filter. Considering the proposed algorithm only remove noise and preserve the uncorrupted information that the algorithm can not only remove noise well but also preserve edge.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.525-539
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• 2007

Consider the regression model $Y_i=g(x_i)+e_i\;for\;i=1,\;2,\;{\ldots},\;n$, where: (1) $x_i$ are fixed design points, (2) $e_i$ are independent random errors with mean zero, (3) g($\cdot$) is unknown regression function defined on [0, 1]. Under $Y_i$ are censored randomly, we discuss the asymptotic normality of the weighted kernel estimators of g when the censored distribution function is known or unknown.

• Journal of the Korean Statistical Society
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• v.18 no.2
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• pp.118-124
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• 1989

In the one-way random effect model, we often estimate the variance components by the ANOVA method and then estimate the population mean. Whe there are only two distint group sizes, the conventional mean estimator is represented as a weighted average of two normal means with weights being the function of variance component estimators. In this paper, we will study a method which can compute the exact variance of the mean estimator when we set the negative variance component estimate to zero.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.27-32
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• 2008

The laminated composite materials have been applied to various mechanical structures due to their high performance to weight ratios. In this study, we suggest a stochastic finite element scheme for the probabilistic analysis of the composite laminated plates. The composite materials consist of two different materials which constitute the matrix and fiber. The material properties in the major and minor directions are determined depending on the volume fraction of these two materials. In this study, the elastic modulus and shear modulus are considered as random and the effect of these random properties on the behavior of the composite plate is investigated. We adopt the weighted integral scheme in the formulation, which has been recognized as the most accurate method in the statistical methodologies. For verification of the proposed scheme, Monte Carlo analysis is also performed for the comparison with the proposed scheme.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.363-370
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• 1995

A famous result of Chow and Robbins [8] asserts that if ${X_n, n \geq 1}$ are independent and identically distributed (i.i.d.) random variables with $E$\mid$X_1$\mid$ = \infty$, then for each sequence of constants ${M_n, n \geq 1}$ either $$ (1) lim inf_{n\to\infty} $\mid$\frac{M_n}{\sum_{j=1}^{n}X_j}$\mid$ = 0 almost certainly (a.c.) $$ or $$ (2) lim sup_{n\to\infty}$\mid$\frac{M_n}{\sum_{j=1}^{n}X_j}$\mid$ = \infty a.c. $$ and thus $P{lim_{n\to\infty} \sum_{j=1}^{n}X_j/M_n = 1} = 0$. Note that both (1) and (2) may indeed prevail.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.261-272
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• 2019

In this paper, we propose a procedure to build a prediction interval of the sum of dependent binary random variables over a graph to account for the dependence among binary variables. Our main interest is to find a prediction interval of the weighted sum of dependent binary random variables indexed by a graph. This problem is motivated by the prediction problem of various elections including Korean National Assembly and US presidential election. Traditional and popular approaches to construct the prediction interval of the seats won by major parties are normal approximation by the CLT and Monte Carlo method by generating many independent Bernoulli random variables assuming that those binary random variables are independent and the success probabilities are known constants. However, in practice, the survey results (also the exit polls) on the election are random and hardly independent to each other. They are more often spatially correlated random variables. To take this into account, we suggest a spatial auto-regressive (AR) model for the surveyed success probabilities, and propose a residual based bootstrap procedure to construct the prediction interval of the sum of the binary outcomes. Finally, we apply the procedure to building the prediction intervals of the number of legislative seats won by each party from the exit poll data in the $19^{th}$ and $20^{th}$ Korea National Assembly elections.