• Journal of the Korean Statistical Society
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• v.24 no.2
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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.

• Korean Journal of Veterinary Research
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• v.50 no.1
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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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• v.6 no.3
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.2
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.1
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• pp.45-53
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• 2015

Large-capacity of household washing machine can become unbalanced during the dehydration process. To solve this problem, several types of suspensions have been installed in a washing machine. In this study, physical tests were carried out on a frictional suspension, and the nonlinear characteristics were modeled by combining several simple physical models. The parameters were estimated based on the least squares solution. The simulation and test results were compared to verify the validity of the friction damper model.

• Management Science and Financial Engineering
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• v.14 no.2
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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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• v.6 no.4
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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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• v.20 no.5
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• pp.879-886
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• 2009

The purpose of this article is to present the application of Least Squares Support Vector Machine in analyzing the existing structure of brand. We estimate the parameters of the Market Share Attraction Model using a non-parametric technique for function estimation called Least Squares Support Vector Machine, which allows us to perform even nonlinear regression by constructing a linear regression function in a high dimensional feature space. Estimation by Least Squares Support Vector Machine technique makes it a good candidate for solving the Market Share Attraction Model. To illustrate the performance of the proposed method, we use the car sales data in South Korea's car market.

• Journal of information and communication convergence engineering
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• v.16 no.1
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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.

• Polymer(Korea)
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• v.39 no.1
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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.