• Communications for Statistical Applications and Methods
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• 제3권3호
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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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• 제29권1_2호
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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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• 제10권2호
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• pp.619-626
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• 2003

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

• 한국신뢰성학회지:신뢰성응용연구
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• 제17권1호
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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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• 제31권2호
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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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• 제9권2호
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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.

• 응용통계연구
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• 제13권2호
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• pp.393-405
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• 2000

원래 최적실험의 이론은 주어진 모형과 그에 따른 가정에 기초하여 발달되었기 때문에 하나의 최적실험기준이 실험이 가족 있는 여러 목적을 모두 반영하는 것이 무리이다. 따라서 실험자가 다목적 실험기준의 필요성을 느끼는 경우에는 종종 여러 최적실험 기준들의 균형을 이루는 방법을 통해 이러한 문제가 다루어진다. 본 연구에서는 이 분산 구조를 가지고 있는 모형을 예를 들어 복합적인 실험기준들을 알아본다. 왜냐하면 이분산인 경우 D-최적과 G-최적실험간의 동격이론은 더 이상 성립되지 않음에 따라 두 실험기준의 특징은 현격하게 구분되어지기 때문이다. 제약조건최적실험, 결합최적실험, 그리고 minimax 설험방법을 통한 실험기준들간의 균형을 꾀하여 보았다. 처음 두 방법은 실험자의 주관이 반영되어 실제적으로 매우 세심한 주의가 필요한 반면, minimax는 그러한 점을 해소하였다고 본다. 또한 이를 확장하여 오차의 이분산 구조에 대한 불확실성이 존재할 때 적용될수 있는 두 가지 실험기준도 마련하여 보았다. 간단한 알고리즘과 결어를 첨부하였다.

• Communications for Statistical Applications and Methods
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• 제22권2호
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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.

• 대한수학회지
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• 제48권6호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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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.