• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.423-429
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• 2014

This paper discusses a method for getting Type I sums of squares by projections under a two-way fixed-effects model when variances of errors are not equal. The method of weighted least squares is used to estimate the parameters of the assumed model. The model is fitted to the data in a sequential manner by using the model comparison technique. The vector space generated by the model matrix can be composed of orthogonal vector subspaces spanned by submatrices consisting of column vectors related to the parameters. It is discussed how to get the Type I sums of squares by using the projections into the orthogonal vector subspaces.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.1
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• pp.97-105
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• 2015

Multiresponse optimization (MRO) seeks to find the setting of input variables, which optimizes the multiple responses simultaneously. The approach of weighted mean squared error (WMSE) minimization for MRO imposes a different weight on the squared bias and variance, which are the two components of the mean squared error (MSE). To date, a weighted sum-based method has been proposed for WMSE minimization. On the other hand, this method has a limitation in that it cannot find the most preferred solution located in a nonconvex region in objective function space. This paper proposes a Tchebycheff metric-based method to overcome the limitations of the weighted sum-based method.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.3
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• pp.300-304
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• 2012

This paper presents a nonlinear observer design method for SOC(state-of-charge) estimation of Lithium polymer battery cell. The dynamic equation of the battery cell is modeled as a simple RC electrical circuit with a nonlinear voltage source and the parameters are obtained via nonlinear optimization. Using the sum of squares decomposition, the observer gain is designed such that the error dynamics is asymptotically stable and the decay rate is below the prescribed value. In order to illustrate the performance of the observer, a computer simulation is performed using the experimental data with the UDDS(urban dynamometer driving schedule) current profile.

• Journal of Animal Science and Technology
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• v.45 no.4
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• pp.509-516
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• 2003

Growth curves were estimated for 1083 female Korean cattle raised in Daekwanryeong branch, National Livestock Research Institute (NLRI). Comparisons were made among various growth curve models for goodness of fit for the growth of the cows. Estimated growth curve functions were $W_t=370.2e^{-2.208e^{-0.00327t}$ for Gompertz model, for von Bertalanffy model, and $W_t=341.2(1+5.652e^{-0.00524t})^{-1}$ for Logistic model. Ages at inflection estimated from Gompertz model, von Bertalanffy model and Logistic model were 242.2 days, 191.5 days, and 330.5 days respectively, body weight at inflection were 136kg, 115kg, and 170kg, and daily gain at inflection were 0.445kg, 0.451kg, and 0.446kg. The predicted weights by ages from Gompertz model, von Bertalanffy model, and Logistic model were onsistently overestimated at birth weight and underestimated at 36 month weight. The von Bertalanffy model which had a variable point of inflection fit the data best.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.1822-1829
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• 2006

본 연구에서는 계산된 유량과 실측 유량을 비교하여 Clark 단위도 방법의 매개변수를 추정하고자 하였다. 오산천과 진위천 상류유역에 대하여 Arcview와 WMS로 지형자료에 대한 전 처리를 한후, HEC-HMS 프로그램을 이용하여 유출량을 산정하였다. 2001년부터 2005년까지 4개의 사상에 대하여 강우량, 기흥저수지와 이동저수지의 실제 방류량을 이용하여 유출량을 산정하였으며, Clark 모형의 매개변수를 Russel 공식, Sabol 공식 및 HEC-HMS 프로그램에 내장된 Nelder-Mead 최적화 방법을 이용하여 매개변수를 각각 산정하여 회화 지점의 실측 유출량과 비교.평가하였다. 빈도가 큰 유출사상의 경우에는 Sabol 식을 적용한 결과가 Russel 식을 적용한 모의결과보다 첨두유량의 재현성이 우수하게 나타났으며, 유출량이 작은 경우에는 Russel 식을 적용한 모의결과가 우수하였다. 첨두가 중제곱평균제곱근오차, 잔차자승의 합, 절대잔차의 합 등 3가지의 서로다른 목적함수를 적용하여 매개변수를 자동 보정하였을 때, 목적함수에 따른 첨두유량의 오차는 거의 동일하였으며, 첨두시간에 대한 오차는 첨두가중제곱평균제곱근오차를 적용했을 때 가장 작은 것으로 분석되었다. 그리고 Clark 유역 추적모형의 자동보정을 통하여 추정한 매개변수인 도달시간과 저류상수는 강우사상에 따라서 변동하는 특성을 나타내기 때문에 최적의 도달시간 및 저류상수는 홍수사상별로 추정되어야 하며 이 결과는 홍수량 산정을 위한 매개변수 추정과정의 비유일성 및 복잡성을 암시하고 있다.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.395-403
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• 2002

In the third phase of the response surface methods, the first-order model is assumed and the curvature of the response surface is checked with a fractional factorial design augmented by centre runs. We further assume that a true model is a quadratic polynomial. To choose an optimal design, Box and Draper(1959) suggested the use of an average mean squared error (AMSE), an average of MSE of y(x) over the region of interest R. The AMSE can be partitioned into the average prediction variance (APV) and average squared bias (ASB). Since AMSE is a function of design moments, region moments and a standardized vector of parameters, it is not possible to select the design that minimizes AMSE. As a practical alternative, Box and Draper(1959) proposed minimum bias design which minimize ASB and showed that factorial design points are shrunk toward the origin for a minimum bias design. In this paper we propose a robust AMSE design which maximizes the minimum efficiency of the design with respect to a standardized vector of parameters.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.493-499
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• 2014

The Pythagorean won-loss formula postulated by James (1980) indicates the percentage of games as a function of runs scored and runs allowed. Several hundred articles have explored variations which improve RMSE by original formula and their fit to empirical data. This paper considers a variation on the formula which allows for variation of the Pythagorean exponent. We provide the most suitable optimal exponent in the Pythagorean method. We compare it with other methods, such as the Pythagenport by Davenport and Woolner, and the Pythagenpat by Smyth and Patriot. Finally, our results suggest that proposed method is superior to other tractable alternatives under criterion of RMSE.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1093-1101
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• 2015

This paper discusses nested design models when nesting occurs in treatment structure and design structure. Some are fixed and others are random; subsequently, the fixed factors having a nested design structure are assumed to be nested in the random factors. The treatment structure can involve random and fixed effects as well as a design structure that can involve several sizes of experimental units. This shows how to use projections for sums of squares by fitting the model in a stepwise procedure. Expectations of sums of squares are obtained via synthesis. Variance components of the nested design model are estimated by the method of moments.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.11-20
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• 2017

In this paper, we introduced linear spatial time series (space-time autoregressive and moving average model) and nonlinear spatial time series (space-time bilinear model). Also we estimated the parameters by Kalman Filter method and made comparative studies of power of forecast in the final model. We proposed several weight matrices such as equal proportion allocation, reciprocal proportion between distances, and proportion of population sizes. For applications, we collected Mumps data at Korea Center for Disease Control and Prevention from January 2001 until August 2008. We compared three approaches of weight matrices using the Mumps data. Finally, we also decided the most effective model based on sum of square forecast error.

• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.271-280
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• 2005

Kriging methods as traditional spatial data analysis methods and geographical weighted regression models as statistical analysis methods are compared. In this paper, we apply data from the Ministry of Environment to spatial analysis for practical study. We compare these methods to performance with monthly carbon monoxide observations taken at 116 measuring area of air pollution in 1999.