• Journal of the Korean Data and Information Science Society
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• 제22권5호
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• pp.999-1005
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• 2011

This paper proposes a weighted least squares support vector machine for asymmetric least squares regression. This method achieves nonlinear prediction power, while making no assumption on the underlying probability distributions. The cross validation function is introduced to choose optimal hyperparameters in the procedure. Experimental results are then presented which indicate the performance of the proposed model.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.133-139
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• 2022

We offered a new method for constructing Latin squares. We introduce the concept of a standard form via example for Latin squares of order n and we also call it symmetric BCL algebras matrix, and thereby become BCL algebra representations of the picture of Latin squares. Our research shows that some new properties of the Latin squares with BCL algebras are in ℤ_n.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.19-34
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• 2016

In this paper, we present a split least-squares characteristic mixed finite element method(MFEM) to get the approximate solutions of the convection dominated Sobolev equations. First, to manage both convection term and time derivative term efficiently, we apply a least-squares characteristic MFEM to get the system of equations in the primal unknown and the flux unknown. Then, we obtain a split least-squares characteristic MFEM to convert the coupled system in two unknowns derived from the least-squares characteristic MFEM into two uncoupled systems in the unknowns. We theoretically prove that the approximations constructed by the split least-squares characteristic MFEM converge with the optimal order in L² and H¹ normed spaces for the primal unknown and with the optimal order in L² normed space for the flux unknown. And we provide some numerical results to confirm the validity of our theoretical results.

• Communications for Statistical Applications and Methods
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• 제13권2호
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• pp.233-241
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• 2006

Classical principal component analysis (PCA) can be formulated as finding the linear subspace that best accommodates multidimensional data points in the sense that the sum of squared residual distances is minimized. As alternatives to such LS (least squares) fitting approach, we produce LMS (least median of squares) and LTS (least trimmed squares)-type PCA by minimizing the median of squared residual distances and the trimmed sum of squares, in a similar fashion to Rousseeuw (1984)'s alternative approaches to LS linear regression. Proposed methods adopt the data-driven optimization algorithm of Croux and Ruiz-Gazen (1996, 2005) that is conceptually simple and computationally practical. Numerical examples are given.

• 대한수학회지
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• 제54권5호
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• pp.1557-1571
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• 2017

The L-curve method is a parametric plot of interrelation between the residual norm of the least squares problem and the solution norm. However, the L-curve method may be hard to apply to the total least squares problem due to its no closed form solution of the regularized total least squares problems. Thus the sequence of the solution norm under the fixed regularization parameter and its corresponding residual need to be found with an efficient manner. In this paper, we suggest an efficient algorithm to find the sequence of the solutions and its residual in order to plot the L-curve for the total least squares problems. In the numerical experiments, we present that the proposed algorithm successfully and efficiently plots fairly 'L' like shape for some practical regularized total least squares problems.

• 대한기계학회논문집A
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• 제25권10호
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• pp.1605-1612
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• 2001

Least-squares meshfree method is presented. Conventional meshfree methods based on the Galerkin formulation suffer from inaccurate numerical integration. Least-squares formulation exhibits rather different integration-related characteristics. It is demonstrated through numerical examples that least-squares formulation is much more robust to integration errors than the Galerkin's. Therefore efficient meshfree methods can be devised by combining very simple integration algorithms and least-squares formulation.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.501-512
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• 1997

In multiple linear regression model we have presupposed assumptions (independence normality variance homogeneity and so on) on error term. When case weights are given because of variance heterogeneity we can estimate efficiently regression parameter using weighted least squares estimator. Unfortunately this estimator is sen-sitive to outliers like ordinary least squares estimator. Thus in this paper we proposed some statistics for detection of outliers in weighted least squares regression.

• Journal of the Korean Statistical Society
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• 제28권2호
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• pp.151-165
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• 1999

This paper considers the trimmed least squares estimator of the autoregression parameter in the unstable AR(1) model: X\ulcorner=ØX\ulcorner+$\varepsilon$\ulcorner, where $\varepsilon$\ulcorner are iid random variables with mean 0 and variance $\sigma$$^2$> 0, and Ø is the real number with │Ø│=1. The trimmed least squares estimator for Ø is defined in analogy of that of Welsh(1987). The limiting distribution of the trimmed least squares estimator is derived under certain regularity conditions.

• 한국수학사학회지
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• 제23권3호
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• pp.21-31
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• 2010

2006년 이전까지도 유럽의 오일러가 직교라틴방진의 첫 연구자로서 인정을 받아왔다. 그러나 오일러 이전에 조선의 최석정이 오일러 이전에 이미 9차의 직교라틴 방진을 만들었다는 사실이 2006년 출판된 '조합론 디자인 편람' 에 소개됨으로써 우리만 알고 있던 사실이 세계적으로 공인되었다. 본 논문에서는 최석정과 양휘산법의 마방진을 비교하고 세계최초로 만들어진 최석정의 직교라틴방진과 오일러 가설의 역사를 설명한다.

• Journal of the Korean Data and Information Science Society
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• 제25권2호
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• pp.423-429
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• 2014

본 논문은 이원고정효과모형의 분산분석에서 오차의 독립성과 등분산성이 만족되지 않는 경우를 가정하고 있다. 자료분석을 위한 모수추정방법으로 가중최소제곱법을 가정하고 있으며 모수를 추정하기 위한 방법으로 모형의 순차적 적합방식을 이용하고 있다. 또한, 모형의 행렬표현식으로부터 벡터공간에서의 사영을 이용하여 자료를 분석하는 방법을 제시하고 있다. 모형의 순차적 적합에 해당하는 제1종 제곱합을 구하기 위하여 모형행렬에 의한 부분공간으로의 사영을 다루고 있다. 이 경우에 사영에 의한 제곱합을 사영제곱합으로 취급한다.