• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.551-561
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• 2001

This paper deals with the asymptotic properties for statistical inferences of the parameters in nonlinear regression models. As an optimal criterion for robust estimators of the regression parameters, the regression quantile method is proposed. This paper defines the regression quintile estimators in the nonlinear models and provides simple and practical sufficient conditions for the asymptotic normality of the proposed estimators when the parameter space is compact. The efficiency of the proposed estimator is especially well compared with least squares estimator, least absolute deviation estimator under asymmetric error distribution.

• Journal of the military operations research society of Korea
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• v.13 no.1
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• pp.91-100
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• 1987

This paper deals with an algorithm for solving nonlinear programming problems with equality constraints. Nonlinear programming problems are transformed into a square sums of nonlinear functions by the Lagrangian multiplier method. And an iteration method minimizing this square sums is suggested and then an algorithm is proposed. Also theoretical basis of the algorithm is presented.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.108-112
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• 1986

Several algorithms for bivariate time series modeling are reviewed : linear least square, nonlinear least squares, generalized least square, and multi-stage least square methods. Estimation results of simulated data by the above methods are discussed.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.315-326
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• 2009

The unknown parameters in regression models are usually estimated by using various existing methods. There are several existing methods, such as the least squares method, which is the most common one, the least absolute deviation method, the regression quantile method, and the asymmetric least squares method. For the nonlinear time series regression models, which do not satisfy the general conditions, we will compare them in two ways: 1) a theoretical comparison in the asymptotic sense and 2) an empirical comparison using Monte Carlo simulation for a small sample size.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.153-165
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• 2003

This paper considers the likelihood ratio test statistic based on nonlinear regression quantiles estimators in order to test of hypothesis about the regression parameter $\theta_o$ and derives asymptotic distribution of proposed test statistic under the null hypothesis and a sequence of local alternative hypothesis. The paper also investigates asymptotic relative efficiency of the proposed test to the test based on the least squares estimators or the least absolute deviation estimators and gives some examples to illustrate the application of the main result.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.1
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• pp.56-67
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• 2012

In this thesis, to compensate the sweep nonlinearity occurring in the high resolution radar system using FMICW or FMCW, the method of the estimation of the nonlinearity is proposed. The nonlinear phase component caused by the nonlinear characteristic of the radar system is modelled as a linear combination of the sinusoidal functions consisting of various magnitudes and phases(systematic nonlinear phase error) and a random component(stochastic nonlinear phase error). From two IF signals that are measured respectively independently for two reference point targets lying in different distances which are known, a sparse linear equation is made and solved by least squares method to estimate the nonlinear phase component. The estimated component can be used for predistortion method to compensate the sweep nonlinearity.

• 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

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.227-230
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• 1996

The paper highlights the need for cautious least squares estimation when dealing with industrial applications of bilinear self-tuning control and indicates in qualitative terms the benefits of the approach over linear self-tuning control schemes. The cautious least squares algorithm is described and the use of cautious self-tuning in the context of both commissioning and implementation discussed.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.337-343
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• 2003

In this paper we present the prediction interval estimation method using bootstrap method for least squares support vector machine(LS-SVM) regression, which allows us to perform even nonlinear regression by constructing a linear regression function in a high dimensional feature space. The bootstrap method is applied to generate the bootstrap sample for estimation of the covariance of the regression parameters consisting of the optimal bias and Lagrange multipliers. Experimental results are then presented which indicate the performance of this algorithm.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1087-1094
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• 2005

e-insensitive support vector regression(e-SVR) is capable of providing more complete description of the linear and nonlinear relationships among random variables. In this paper we propose an iterative reweighted least squares(IRWLS) procedure to solve the quadratic problem of e-SVR with a modified loss function. Furthermore, we introduce the generalized approximate cross validation function to select the hyperparameters which affect the performance of e-SVR. Experimental results are then presented which illustrate the performance of the IRWLS procedure for e-SVR.