• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.40 no.4
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• pp.315-324
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• 2022

The conventional LESS (LEast-Squares Solution) is calculated under the assumption that there is no errors in independent variables. However, the coordinates of a point, either from traditional ground surveying such as slant distances, horizontal and/or vertical angles, or GNSS (Global Navigation Satellite System) positioning, cannot be determined independently (and the components are correlated each other). Therefore, the TLS (Total Least Squares) adjustment should be applied for all applications related to the coordinates. Many approaches were suggested in order to solve this problem, resulting in equivalent solutions except some restrictions. In this study, we calculated the normal vector of the 3D plane determined by the trace of the VLBI targets based on TLS within GHM (Gauss-Helmert Model). Another numerical test was conducted for the estimation of the Helmert transformation parameters. Since the errors in the horizontal components are very small compared to the radius of the circle, the final estimates are almost identical. However, the estimated variance components are significantly reduced as well as show a different characteristic depending on the target location. The Helmert transformation parameters are estimated more precisely compared to the conventional LESS case. Furthermore, the residuals can be predicted on both reference frames with much smaller magnitude (in absolute sense).

• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.159-168
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• 2008

Since the term structure of interest rates (TSIR) has longitudinal data, we should consider as input variables both time left to maturity and time simultaneously to get a more useful and more efficient function estimation. However, since the resulting data set becomes very large, we need to develop a fast and reliable estimation method for large data set. Furthermore, it tends to overestimate TSIR because data are correlated. To solve these problems we propose a mixture of weighted least squares support vector machines. We recognize that the estimate is well smoothed and well explains effects of the third stock market crash in USA through applying the proposed method to the US Treasury bonds data.

• The Korean Journal of Applied Statistics
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• v.27 no.4
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• pp.553-560
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• 2014

This paper deals with estimable functions of parameters of less than full rank linear model. In general, the parameters of an overspecified model are not uniquely determined by least squares solutions. It discusses how to formulate linear estimable functions as functions of parameters in the model and shows how to use projection matrices to check out whether a parameter or function of the pamameters is estimable. It also presents a method to form a basis set of estimable functions using linearly independent characteristic vectors generating the row space of the model matrix.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.431-440
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• 2013

We consider the problem of estimating the parameters of heavy tailed distributions. In general, maximum likelihood estimation(MLE) is the most preferred method of parameter estimation because it has good properties such as asymptotic consistency, normality and efficiency. However, MLE is not always the best solution because MLE is unstable or does not exist in some cases. This paper proposes another parameter estimation method, non-linear least squares(NLS) and compares its performance to MLE. The NLS estimator is achieved by minimizing sum of squared difference between empirical cumulative distribution function(CDF) and a theoretical distribution function. In this article, we compare the NLS method to MLE using simulated data from heavy tailed distributions. The NLS method is shown to perform better than MLE in Burr distribution when the sample size is small; in addition, it performs well in a Frechet distribution.

• Proceedings of the Korea Water Resources Association Conference
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• 2002.05a
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• pp.541-546
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• 2002

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1155-1163
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• 2016

This paper deals with an estimation procedure of variance components in a mixed effects model by projections. Projections are used to obtain sums of squares instead of using reductions in sums of squares due to fitting both the assumed model and sub-models in the fitting constants method. A projection matrix can be obtained for the residual model at each step by a stepwise procedure to test the hypotheses. A weighted least squares method is used for the estimation of fixed effects. Satterthwaite's approximation is done for the confidence intervals for variance components.

• Journal of the Korean Chemical Society
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• v.23 no.2
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• pp.104-110
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• 1979

A new least square method for analysis of the whole time course of enzyme-catalyzed reactions is presented. This method requires only a programmable calculator with small capacity and is applicable to both uninhibited reactions and reactions inhibited by products or added compounds. This method fits the data to the nonlinear plot of substrate concentration vs. time, and, consequently, estimates the kinetic parameters better than the least square method based on linearly transformed equations.

• 한국공간정보시스템학회:학술대회논문집
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• 2005.11a
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• pp.35-39
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• 2005

선형혼합분광분석(LSU, Linear Spectral Unmixing) 모델은 위성 영상의 한 화소 값이 공간 내에 포함된 다양한 지표 대상물의 반사에너지가 혼합된 결과로 나타난다는 가정을 통해 화소이하(Sub-Pixel) 단위의 영상 분석을 수행하는 알고리즘의 한 형태이다. 분석의 결과는 한 화소에 존재하는 순수 대상물(Endmember)의 비율로 나타나며, 최소제곱법을 이용하여 결과를 도출하는 것이 일반적인 방법으로 알려져 있다. 하지만, 최소제곱법을 이용한 선형혼합분광분석모델은 기본적인 가정을 만족시키지 못하며, Endmember를 사용자가 임의로 지정해야 하기 때문에 영상 분석에 많은 어려움이 있다. 이런 단점을 극복하기 위해 무감독으로 추출된 Endmember를 이용한 제약선형분광혼합분석(Constrained Linear Spectral Unmixing) 모델을 본 연구를 통해 제안하고자 한다. 결과를 통해, 무감독 제약선형분광혼합분석 모델은 선형분광혼합분석 모델에 비해 각각의 Endmember에 대하여 제약조건을 만족하는 점유비율(Abundance) 정보를 제공하였으나, 비슷한 Endmember를 중복 추출할 수 있는 가능성도 지니고 있음을 확인할 수 있었다.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.247-253
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• 1998

In ease of the epidemic Zero-Inflated Poisson model, likelihood ratio test was used for testing epidemic alternatives. Epidemic changepoints were estimated by the method of least squares. It were used for starting points to estimate the maximum likelihood estimators. And several parameters were compared through the Monte Carlo simulations. As a result, maximum likelihood estimators for the epidemic chaagepoints and several parameters are better than the least squares and moment estimators.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.11
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• pp.2312-2321
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• 2002

The first-order least-squares meshfree method for linear elasticity is presented. The conventional and the compatibility-imposed least-squares formulations are studied on the convergence behavior of the solution and the robustness to integration error. Since the least-squares formulation is a type of mixed formulation and induces positive-definite system matrix, by using shape functions of same order for both primal and dual variables, higher rate of convergence is obtained for dual variables than Galerkin formulation. Numerical examples also show that the presented formulations do not exhibit any volumetric locking for the incompressible materials.