• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.889-898
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• 2002

In decision theoretic estimation, the loss function usually emphasizes precision of estimation. However, one may have interest in goodness of fit of the overall model as well as precision of estimation. From this viewpoint, Zellner(1994) proposed the balanced loss function which takes account of both "goodness of fit" and "precision of estimation". This paper considers estimation of the parameter of a Bernoulli distribution using Zellner's(1994) balanced loss function. It is shown that the sample mean $\overline{X}$, is admissible. More general results, concerning the admissibility of estimators of the form $a\overline{X}+b$ are also presented. Finally, minimax estimators and some numerical results are given at the end of paper,at the end of paper.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.355-367
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• 2010

In this paper, the existence of periodic solutions is obtained for a kind of p-Laplacian systems by the minimax methods in critical point theory. Moreover, the existence of infinite periodic solutions is also obtained.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.669-684
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• 2012

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of degenerate Dirichlet problem in the case near resonance.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.487-500
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• 1999

We propose a class of hierarchical Bayes estimators of the error variance under the relative squared error loss in balanced fixed-effects two-way analysis of variance models. Also we provide analytic expressions for the risk improvement of the hierarchical Bayes estimators over multiples of the error sum of squares. Using these expressions we identify a subclass of the hierarchical Bayes estimators each member of which dominates the best multiple of the error sum of squares which is known to be minimax. Numerical values of the percentage risk improvement are given in some special cases.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.347-371
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• 2021

A plethora of applications from mathematical programmings, such as minimax, mathematical programming, penalization and fixed point problems can be framed as variational inequality problems. Most of the methods that used to solve such problems involve iterative methods, that is why, in this paper, we introduce a new extragradient-like method to solve pseudomonotone variational inequalities in a real Hilbert space. The proposed method has the advantage of a variable step size rule that is updated for each iteration based on previous iterations. The main advantage of this method is that it operates without the previous knowledge of the Lipschitz constants of an operator. A strong convergence theorem for the proposed method is proved by letting the mild conditions on an operator 𝒢. Numerical experiments have been studied in order to validate the numerical performance of the proposed method and to compare it with existing methods.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.53-64
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• 2022

High dimensional time series is gaining considerable attention in recent years. The sparse vector heterogeneous autoregressive (VHAR) model proposed by Baek and Park (2020) uses adaptive lasso and debiasing procedure in estimation, and showed superb forecasting performance in realized volatilities. This paper extends the sparse VHAR model by considering non-convex penalties such as SCAD and MCP for possible bias reduction from their penalty design. Finite sample performances of three estimation methods are compared through Monte Carlo simulation. Our study shows first that taking into cross-sectional correlations reduces bias. Second, nonconvex penalties performs better when the sample size is small. On the other hand, the adaptive lasso with debiasing performs well as sample size increases. Also, empirical analysis based on 20 multinational realized volatilities is provided.

• Journal of the Korean Society of Marine Environment & Safety
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• v.17 no.2
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• pp.131-136
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• 2011

The furrow calculation and traffic measurement of sailing ship using computer vision are useful methods to prevent maritime accident by predicting the possibility of an accident occurrence in advance. In this paper, sailing ships are recognized using image erosion, differential operator and minimax value, which can be verified directly because the calculated coordinates are displayed on electronic navigation chart. The developed algorithm based on area information of this paper has the advantage which is compared to the conventional radar system focused on point information.

• Communications for Statistical Applications and Methods
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• v.29 no.5
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• pp.591-601
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• 2022

In gene set analysis with microarray expression data, a group of genes such as a gene regulatory pathway and a signaling pathway is often tested if there exists either differentially expressed (DE) or differentially co-expressed (DC) genes between two biological conditions. Recently, a statistical test based on covariance estimation have been proposed in order to identify DC genes. In particular, covariance regularization by hard thresholding indeed improved the power of the test when the proportion of DC genes within a biological pathway is relatively small. In this article, we compare covariance thresholding methods using four different regularization penalties such as lasso, hard, smoothly clipped absolute deviation (SCAD), and minimax concave plus (MCP) penalties. In our extensive simulation studies, we found that both SCAD and MCP thresholding methods can outperform the hard thresholding method when the proportion of DC genes is extremely small and the number of genes in a biological pathway is much greater than a sample size. We also applied four thresholding methods to 3 different microarray gene expression data sets related with mutant p53 transcriptional activity, and epithelium and stroma breast cancer to compare genetic pathways identified by each method.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.547-572
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• 2010

We study existence of positive solutions of the classical nonlinear Schr$\ddot{o}$dinger equation $-{\Delta}u\;+\;V(x)u\;-\;f(x,\;u)\;-\;H(x)u^{2*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$. In fact, we consider the following more general quasi-linear Schr$\ddot{o}$odinger equation $-div(|{\nabla}u|^{m-2}{\nabla}u)\;+\;V(x)u^{m-1}$ $-f(x,\;u)\;-\;H(x)u^{m^*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$, where m $\in$ (1, n) is a positive number and $m^*\;:=\;\frac{mn}{n-m}\;>\;0$, is the corresponding critical Sobolev embedding number in $\mathbb{R}^n$. Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.129-140
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• 2020

In this paper, we introduce an efficient algorithm for the non-convex penalized multinomial logistic regression that can be uniformly applied to a class of non-convex penalties. The class includes most non-convex penalties such as the smoothly clipped absolute deviation, minimax concave and bridge penalties. The algorithm is developed based on the concave-convex procedure and modified local quadratic approximation algorithm. However, usual quadratic approximation may slow down computational speed since the dimension of the Hessian matrix depends on the number of categories of the output variable. For this issue, we use a uniform bound of the Hessian matrix in the quadratic approximation. The algorithm is available from the R package ncpen developed by the authors. Numerical studies via simulations and real data sets are provided for illustration.