• Survey Research
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• v.7 no.2
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• pp.53-69
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• 2006

Weights can be made and imposed in both sample design stage and analysis stage in a sample survey. While in design stage weights are related with sample data acquisition quantities such as sample selection probability and response rate, in analysis stage weights are connected with external quantities, for instance population quantities and some auxiliary information. The final weight is the product of all weights in both stage. In the present paper, we focus on the weight in analysis stage and investigate the effect of such weights imposed on the weighted mean when estimating the population mean. We consider a finite population with a pair of fixed survey value and weight in each unit, and suppose equal selection probability designs. Under the condition we derive the formulas of the bias as well as mean square error of the weighted mean and show that the weighted mean is biased and the direction and amount of the bias can be explained by the correlation between survey variate and weight: if the correlation coefficient is positive, then the weighted mein over-estimates the population mean, on the other hand, if negative, then under-estimates. Also the magnitude of bias is getting larger when the correlation coefficient is getting greater. In addition to theoretical derivation about the weighted mean, we conduct a simulation study to show quantities of the bias and mean square errors numerically. In the simulation, nine weights having correlation coefficient with survey variate from -0.2 to 0.6 are generated and four sample sizes from 100 to 400 are considered and then biases and mean square errors are calculated in each case. As a result, in the case or 400 sample size and 0.55 correlation coefficient, the amount or squared bias of the weighted mean occupies up to 82% among mean square error, which says the weighted mean might be biased very seriously in some cases.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.281-290
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• 2007

Linear estimator, a weighted sum of the sample observation, is commonly adopted to estimate the finite population parameters such as population totals in survey sampling. The weight for a sampled unit is often constructed by multiplying the base weight, which is the inverse of the first-order inclusion probability, by an adjustment term that takes into account of the auxiliary information obtained throughout the population. The linear estimator using the weight adjustment is often more efficient than the one using only the bare weight, but its valiance estimation is more complicated. We discuss variance estimation for a general class of weight-adjusted estimator. By identifying that the weight-adjusted estimator can be viewed as a function of estimated nuisance parameters, where the nuisance parameters were used to incorporate the auxiliary information, we derive a linearization of the weight-adjusted estimator using a Taylor expansion. The method proposed here is quite general and can be applied to wide class of the weight-adjusted estimators. Some examples and results from a simulation study are presented.

• Proceedings of the Korean Association for Survey Research Conference
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• 2002.11a
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• pp.255-274
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• 2002

We classify rotation sampling designs into two classes. The first class replaces sample units within the same rotation group while the second class replaces sample units between different rotation groups. The first class is specified by the three-way balanced design which is a multi-level version of previous balanced designs. We introduce an extended generalized composite estimator (EGCE) and derive its variance and mean squared error for each of the two classes of design, cooperating two types of correlations and three types of biases. Unbiased estimators are derived for difference between interview time biases, between recall time biases, and between rotation group biases. Using the variance and mean squared error, since any rotation design belongs to one of the two classes and the EGCE is a most general estimator for rotation design, we evaluate the efficiency of EGCE to simple weighted estimator and the effects of levels, design gaps, and rotation patterns on variance and mean squared error.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.595-611
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• 2016

We use nonlinear regression models (such as the Hill Model) when we analyze data in toxicology and/or pharmacology. In nonlinear regression models an estimator of parameters and estimation of measurement about uncertainty of the estimator are influenced by the variance structure of the error. Thus, estimation methods should be different depending on whether the data are homoscedastic or heteroscedastic. However, we do not know the variance structure of the error until we actually analyze the data. Therefore, developing estimation methods robust to the variance structure of the error is an important problem. In this paper we propose a method to estimate parameters in nonlinear regression models based on a preliminary test. We define an estimator which uses either the ordinary least square estimation method or the iterative weighted least square estimation method according to the results of a simple preliminary test for the equality of the error variance. The performance of the proposed estimator is compared to those of existing estimators by simulation studies. We also compare estimation methods using real data obtained from the National Toxicology program of the United States.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.11
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• pp.2108-2116
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• 2008

The paper concerns Fuzzy C-Means clustering based Radial Basis Function neural networks (FCM-RBFNN) and the optimization of the network is carried out by means of Particle Swarm Optimization(PSO). FCM-RBFNN is the extended architecture of Radial Basis Function Neural Network(RBFNN). In the proposed network, the membership functions of the premise part of fuzzy rules do not assume any explicit functional forms such as Gaussian, ellipsoidal, triangular, etc., so its resulting fitness values directly rely on the computation of the relevant distance between data points by means of FCM. Also, as the consequent part of fuzzy rules extracted by the FCM - RBFNN model, the order of four types of polynomials can be considered such as constant, linear, quadratic and modified quadratic. Weighted Least Square Estimator(WLSE) are used to estimates the coefficients of polynomial. Since the performance of FCM-RBFNN is affected by some parameters of FCM-RBFNN such as a specific subset of input variables, fuzzification coefficient of FCM, the number of rules and the order of polynomials of consequent part of fuzzy rule, we need the structural as well as parametric optimization of the network. In this study, the PSO is exploited to carry out the structural as well as parametric optimization of FCM-RBFNN. Moreover The proposed model is demonstrated with the use of numerical example and gas furnace data set.

• Wind and Structures
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• v.11 no.1
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• pp.19-33
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• 2008

This research investigates the adaptive input estimation method applied to the multilayer shearing stress structure. This method is to estimate the values of wind load inputs by analyzing the active reaction of the system. The Kalman filter without the input term and the adaptive weighted recursive least square estimator are two main portions of this method. The innovation vector can be produced by the Kalman filter, and be applied to the adaptive weighted recursive least square estimator to estimate the wind load input over time. This combined method can effectively estimate the wind loads to the structure system to enhance the reliability of the system active performance analysis. The forms of the simulated inputs (loads) in this paper include the periodic sinusoidal wave, the decaying exponent, the random combination of the sinusoidal wave and the decaying exponent, etc. The active reaction computed plus the simulation error is regard as the simulated measurement and is applied to the input estimation algorithm to implement the numerical simulation of the inverse input estimation process. The availability and the precision of the input estimation method proposed in this research can be verified by comparing the actual value and the one obtained by numerical simulation.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.7 no.3
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• pp.132-136
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• 2014

We introduce a new architecture of TSK-based fuzzy inference system. The proposed model used fuzzy c-means clustering method(FCM) for efficient disposal of data. The premise part of fuzzy rules don't assume any membership function such as triangular, gaussian, ellipsoidal because we construct the premise part of fuzzy rules using FCM. As a result, we can reduce to architecture of model. In this paper, we are able to use four types of polynomials as consequence part of fuzzy rules such as simplified, linear, quadratic, modified quadratic. Weighed Least Square Estimator are used to estimates the coefficients of polynomial. The proposed model is evaluated with the use of Boston housing data called Machine Learning dataset.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.981-989
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• 2010

In this study, we introduce a new architecture of fuzzy inference system. In the fuzzy inference system, we use Fuzzy C-Means clustering algorithm to form the premise part of the rules. The membership functions standing in the premise part of fuzzy rules do not assume any explicit functional forms, but for any input the resulting activation levels of such radial basis functions directly depend upon the distance between data points by means of the Fuzzy C-Means clustering. As the consequent part of fuzzy rules of the fuzzy inference system (being the local model representing input output relation in the corresponding sub-space), four types of polynomial are considered, namely constant, linear, quadratic and modified quadratic. This offers a significant level of design flexibility as each rule could come with a different type of the local model in its consequence. Either the Least Square Estimator (LSE) or the weighted Least Square Estimator (WLSE)-based learning is exploited to estimate the coefficients of the consequent polynomial of fuzzy rules. In fuzzy modeling, complexity and interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. The performance of the fuzzy inference system is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules(clusters) and the order of polynomial in the consequent part of the rules. Accordingly we can obtain preferred model structure through an adjustment of such parameters of the fuzzy inference system. Moreover the comparative experimental study between WLSE and LSE is analyzed according to the change of the number of clusters(rules) as well as polynomial type. The superiority of the proposed model is illustrated and also demonstrated with the use of Automobile Miles per Gallon(MPG), Boston housing called Machine Learning dataset, and Mackey-glass time series dataset.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.10
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• pp.1171-1179
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• 2012

In this study, we consider a dynamic positioning system (DPS) design problem that can be extended to many application fields. Toward this end, tracking and positioning control problems are discussed. In particular, we design a tracking control system that incorporates an observer based on the 2-DOF servo system design approach in order to obtain the desired state information. In the case of observer design, a weighted $H_{\infty}$ error bound approach for a state estimator is considered. Based on an algebraic Riccati equation (inequality) approach, a necessary and sufficient condition for the existence of a full-order estimator that satisfies the weighted $H_{\infty}$ error bound is introduced. The condition for the existence of the estimator is denoted by a linear matrix inequality (LMI) that yields an optimized solution and the observer gain.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.357-361
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• 2010

미래의 연별 최대 강수량 예측의 정확성을 향상시키는데 역사적 자료가 도움이 된다는 많은 연구 결과가 있었다. 관측의 오차와 자료의 손실로 역사자료를 이용한 강수 예측 방법은 절단자료의 분석을 중심으로 연구되었다. 대표적인 역사자료의 이용방법으로 조건부 적률을 이용한 B17B [Interagency Committee in Water Data, 1982], 조건부적률과적률 관계식을 이용한 Expected Moment Algorithm(EMA) [Cohn et al.;1997], 조건부 확률가중적률을 이용한 Partial Probability Weighted Moment (PPWM)[Wang ; 1991] 방법이 있다. 본 연구에서는 역사적 자료를 반영하는 방법에 있어 B17B와 EMA의 관계를 밝히고 그러한 관계가 PPWM에 동일하게 적용할 수 있음을 보였다. 우리는 B17B와 EMA의 관계를 적률방정식으로 표현하였고 PPWM에서 확률가중 적률 방정식을 정의함으로써 PPWM을 확장하였다. 본 연구에서 제안한 새로운 역사 자료를 이용한 강수예측 방법론을 Expected Probability Weighted Momemt (EPWM) 방법이라고 부르고 그 예측 방법의 성능을 다른 예측방법과 시뮬레이션 결과를 통해 비교하였다. 역사 자료 방법론의 비교는 Generalized Extreme Value (GEV) 분포를 이용하여 이루어졌으며, 각 방법론은 GEV분포의 형태모수(shape parameter)따라 다른 특성을 나타난다는 것을 보였다. 뿐만 아니라 여기서 제안한 EPWM 방법은 대부분의 경우에 좋은 추정량을 준다는 것을 보였다.