• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.303-312
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• 1995

We consider the following type of general semi-parametric non-linear regression model : $y_i = f_i(\theta) + \epsilon_i, i=1, \cdots, n$ where ${f_i(\cdot)}$ represents the set of non-linear functions of the unknown parameter vector $\theta' = (\theta_1, \cdots, \theta_p)$ and ${\epsilon_i}$ represents the set of measurement errors with unknown distribution. Under suitable finite-sample, small-dispersion asymptotic framework, we derive a general lower bound for the asymptotic mean squared error (AMSE) matrix of the Gauss-consistent estimator of $\theta$. We then prove the fundamental result that the general non-linear least squares estimator (NLSE) is an optimal estimator within the class of all regular Gauss-consistent estimators irrespective of the type of the distribution of the measurement errors.

• 대한수의학회지
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• 제50권1호
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• pp.11-17
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• 2010

Linear and non-linear regressions were used to derive the calibration function for the measurement of roxithromycin plasma concentration. Their results were compared with weighted least squares regression by usual weight factors. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = ax$^{b}$ + c (b $\neq$ 1) is compared with the commonly used linear equation, y = ax + b, as well as the quadratic equation, y = ax$^{2}$+ bx + c. In the calibration curve (range of 0.01 to 10 ${\mu}g/mL$) of roxithromycin, both heteroscedasticity and nonlinearity were present therefore linear least squares regression methods could result in large errors in the determination of roxithromycin concentration. By the non-linear and weighted least squares regression, the accuracy of the analytical method was improved at the lower end of the calibration curve. This study suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low dose calibration data which exhibit slight curvature.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.757-770
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• 1999

We analyse in this paper the possibility of using preconditioning techniques as for square non-singular systems, also in the case of inconsistent least-squares problems. We find conditions in which the minimal norm solution of the preconditioned least-wquares problem equals that of the original prblem. We also find conditions such that thd Kaczmarz-Extendid algorithm with relaxation parameters (analysed by the author in [4]), cna be adapted to the preconditioned least-squares problem. In the last section of the paper we present numerical experiments, with two variants of preconditioning, applied to an inconsistent linear least-squares model probelm.

• 제어로봇시스템학회논문지
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• 제10권2호
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• pp.185-191
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• 2004

Partial least squares(PLS) is one of multiplicate statistical process methods and has been developed in various algorithms with the characteristics of principal component analysis, dimensionality reduction, and analysis of the relationship between input variables and output variables. But it has been limited somewhat by their dependency on linear mathematics. The algorithm is proposed to classify for the non-linear data using PLS and the residual compensator(RC) based on radial basis function network (RBFN). It compensates for the error of the non-linear data using the RC based on RBFN. The experimental result is given to verify its efficiency compared with those of previous works.

• 대한기계학회논문집A
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• 제39권1호
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• pp.45-53
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• 2015

세탁기의 용량이 커지면서 세탁 및 탈수 시의 세탁물에 의한 질량 불균형 문제가 심해지고 있으며, 이러한 문제를 해결하기 위하여 세탁기에서도 다양한 형태의 서스펜션이 장착되고 있다. 본 연구에서는 마찰 서스펜션에서 발생하는 힘을 측정한 뒤, 물리적인 수식으로 마찰 서스펜션의 비선형 특성을 모델링 하였다. 최소 자승 해(least squares solution)를 구해 파라미터들을 추정하고, 시험과 동일한 조건의 시뮬레이션을 실시하여 개발된 마찰 서스펜션 모델링의 타당성을 검증하였다.

• Management Science and Financial Engineering
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• 제14권2호
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• pp.89-104
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• 2008

Growth curves including Bass, Logistic and Gompertz functions are widely used in forecasting the market demand. Nonlinear least square method is often adopted for estimating the model parameters but it is difficult to set up the starting value for each parameter. If a wrong starting point is selected, the result may lead to erroneous forecasts. This paper proposes a method of selecting starting values for model parameters in estimating some growth curves by nonlinear least square method through grid search and transformation into linear regression model. Resealing the market data using the national economic index makes it possible to figure out the range of parameters and to utilize the grid search method. Application to some real data is also included, where the performance of our method is demonstrated.

• Journal of Positioning, Navigation, and Timing
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• 제6권4호
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• pp.141-147
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• 2017

In this paper, an efficient and robust localization algorithm using Receiver Signal Strength Difference (RSSD) for a non-cooperative RF emitter is given. The proposed algorithm firstly calculate the center point and radius of Apollonius's circles and then estimate the intersection point of the circles based on Time of Arrival concept. And this paper also compares the performance of RSSD localization algorithms such as Non-linear Least Squares and Linearized Least Squares by Lines of Position (LOP) with the proposed algorithm. And some conclusions have been reached regarding the relative accuracy, robustness and computational cost of these algorithms.

• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.879-886
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• 2009

본 논문에서는 시장점유율을 추정할 때 최소제곱 서포트벡터기계를 적용하여 보통최소제곱과 최소제곱 서포트벡터기계의 성능을 비교하고자 한다. 최소제곱 서포트벡터기계는 커널 함수를 사용함으로 고차원의 특징 공간에서 선형회귀로 재구성함으로 비선형 회귀문제까지도 해결할 수 있는 장점을 가지고 있다. 그래서 본 논문에서는 비모수 기법인 최소제곱 서포트벡터기계를 이용하여 시장점유율 모형을 추정하고자 한다. 최소제곱 서포트벡터기계를 기반으로 한 모형 추정은 시장점유율 유인모형을 해결하기 위한 좋은 대안이 된다. 최소제곱 서포트벡터기계의 성능을 평가하기 위해 비교 실험에서는 한국 자동차 시장에서 차량 판매량을 이용하여 브랜드별 시장점유율 모형을 추정하였다.

• Journal of information and communication convergence engineering
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• 제16권1호
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• pp.17-22
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• 2018

In massive multiple-input multiple-output (MIMO) systems, linear channel estimation algorithms are widely applied owing to their simple structures. However, they may cause pilot contamination, which affects the subsequent data detection performance. Therefore, herein, for an uplink multicell massive multiuser MIMO system, we consider using an alternating projection (AP) for channel estimation to eliminate the effect of pilot contamination and improve the performance of data detection in terms of the bit error rates as well. Even though the AP is nonlinear, it iteratively searches the best solution in only one dimension, and the computational complexity is thus modest. We have analyzed the mean square error with respect to the signal-to-interference ratios for both the cooperative and non-cooperative multicell scenarios. From the simulation results, we observed that the channel estimation results via the AP benefit the following signal detection more than that via the least squares for both the cooperative and non-cooperative multicell scenarios.

• 폴리머
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• 제39권1호
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• pp.13-22
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• 2015

A new methacrylate copolymer that includes chalcone as a side group, poly(4-methacryloyloxyphenyl-4'-methoxystyryl ketone-co-styrene) was synthesized by free radical copolymerization. FTIR and $^1H$ NMR spectroscopic techniques were used to characterize the homopolymers and copolymers. The copolymerizations were carried out to high conversions. Copolymer compositions were established by $^1H$ NMR spectra analysis. The monomer reactivity ratios for copolymer system were determined by the linearized Kelen $T{\ddot{u}}d{\ddot{o}}s$, and Extended Kelen $T{\ddot{u}}d{\ddot{o}}s$ methods and a non-linear least squares method. The molecular weights and polydispersity index of copolymers were measured by using the gel permeation chromatography (GPC). The effect of copolymer compositions on their thermal behavior were studied by differential scanning calorimetry and thermogravimetric analysis methods. The optical properties of the resulting copolymer were also investigated.