• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.93-101
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• 1996

The unknown response function is usually approximated by a low order polynomial model. Such an approximation always accompanies bias due to model departure. The minimax Average MSE (AMSE) designs are suggested for estimating mean responses. A class of first order minimax AMSE designs is derived and a specific first order minimax AMSE design is selected from the class by optimizing the secondary criterion related to the power of the lack of fit test.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.39-48
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• 2011

Some existence theorems are obtained for periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian by the minimax methods in critical point theory.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.619-626
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• 2003

Given a prior guess for the unknown value of P(Y

• Journal of Applied Reliability
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• v.17 no.1
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• pp.58-65
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• 2017

Different from general operating policies applied for various waiting line situations, two complementary dyadic operating policies are applied alternatingly to a single server maintenance service center model. That is, either of the two dyadic Min (N, T) or Max (N, T) policy is applied to operate such center first and the other operating policy should be applied later, and then the same sequence of both operating policies is followed repeatedly. This operating policy is denoted by the Minimax (N, T) policy. Purpose: Because of the newly introduced operating policy, important system characteristics of the considered service center model such as the expected busy and idle periods, the expected number of customers in the service center and so on should be derived to provide necessary information for determination of the optimal operating policy. Methods: Based on concepts of the newly introduced Minimax (N, T) policy, all necessary system characteristics should be redefined and then derived by constructing appropriate relations between complementary two dyadic operating policies. Results: Desired system characteristics are obtained successfully using simple procedures developed by utilizing peculiar structure of the Minimax (N, T) policy. Conclusion: Applying Minimax (N, T) operating policy is equivalent to applying the simple N and T operating policies alternatingly.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.163-175
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• 2002

An extended version of the minimax eccentricity factor estimation for multiple set case is proposed. In addition, two more simple methods for multiple set factor analysis exploiting the concept of generalized canonical correlation analysis is suggested. Finally, a certain connection between the generalized canonical correlation analysis and the multiple set factor analysis is derived which helps us clarify the relationship.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.315-324
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• 2002

For estimating the error variance under the relative squared error loss in two-way analysis of variance models, we provide a class of hierarchical Bayes estimators and then derive 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. We also identify a subclass of non-minimax hierarchical Bayes estimators.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.393-405
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• 2000

Box and Draper( 19(5) listed some properties of a design that should be considered in design selection. But it is impossible that one design criterion from optimal experimental design theory reflects many potential objectives of an experiment, because the theory was originally based on the underlying model and its strict assumption about the error structure. Therefore, when it is neces::;ary to implement multi-objective experimental design. it is common practice to balance out the several optimal design criteria so that each design criterion involved benefits in terms of its relative "high" efficiency. In this study, we proposed several composite design criteria taking the case of heteroscedastic model. WVhen the heteroscedasticity is present in the model. the well known equivalence theorem between 1)- and C-optimality no longer exists and furthermore their design characteristics are sometimes drastically different. We introduced three different design criteria for this purpose: constrained design, combined design, and minimax design criteria. While the first two methods do reflect the prior belief of experimenter, the last one does not take it into account. which is sometimes desirable. Also we extended this method to the case when there are uncertainties concerning the error structure in the model. A simple algorithm and concluslOn follow.On follow.

• Communications for Statistical Applications and Methods
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• v.22 no.2
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• pp.147-157
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• 2015

We consider a sparse high-dimensional linear regression model. Penalized methods using LASSO or non-convex penalties have been widely used for variable selection and estimation in high-dimensional regression models. In penalized regression, the selection and prediction performances depend on which penalty function is used. For example, it is known that LASSO has a good prediction performance but tends to select more variables than necessary. In this paper, we propose an additive sparse penalty for variable selection using a combination of LASSO and minimax concave penalties (MCP). The proposed penalty is designed for good properties of both LASSO and MCP.We develop an efficient algorithm to compute the proposed estimator by combining a concave convex procedure and coordinate descent algorithm. Numerical studies show that the proposed method has better selection and prediction performances compared to other penalized methods.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1269-1283
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• 2011

For a class of quasilinear elliptic equations we establish the existence of multiple solutions by variational methods.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.81-90
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• 2002

The least informative (favorable) distributions, minimizing Fisher information for a multivariate location parameter, are derived in the parametric class of the exponential-power spherically symmetric distributions under the following characterizing restrictions; (i) a bounded variance, (ii) a bounded value of a density at the center of symmetry, and (iii) the intersection of these restrictions. In the first two cases, (i) and (ii) respectively, the least informative distributions are the Gaussian and Laplace, respectively. In the latter case (iii) the optimal solution has three branches, with relatively small variances it is the Gaussian, them with intermediate variances. The corresponding robust minimax M-estimators of location are given by the $L_2$-norm, the $L_1$-norm and the $L_{p}$ -norm methods. The properties of the proposed estimators and their adaptive versions ar studied in asymptotics and on finite samples by Monte Carlo.