• Journal of the Korea Society for Simulation
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• v.9 no.3
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• pp.43-51
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• 2000

In regression model, we estimate the unknown parameters by using various methods. There are the least squares method which is the most general, the least absolute deviation method, the regression quantile method and the asymmetric least squares method. In this paper, we will compare each others with two cases: firstly the theoretical comparison in the asymptotic sense and then the practical comparison using Monte Carlo simulation for a small sample size.

• Proceedings of the Korea Society for Simulation Conference
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• 2000.11a
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• pp.6-10
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• 2000

In regression model we estimate the unknown parameters using various methods. There are the least squares method which is the most general, the least absolute deviation, the regression quantile and the asymmetric least squares method. In this paper, we will compare each others with two case: to begin with the theoretical comparison in the asymptotic sense, and then the practical comparison using Monte Carlo simulation for a small sample size.

• 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 Korean Statistical Society
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• v.18 no.1
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• pp.46-61
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• 1989

This paper is concerned with the development of a nonparametric procedure for the statistical inference about the nonlinear regression parameters. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both under the null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• 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.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.453-463
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• 1997

Nonparametric kernel regression has recently gained widespread acceptance as an attractive method for the nonparametric estimation of the mean function from noisy regression data. Also, the practical implementation of kernel method is enhanced by the availability of reliable rule for automatic selection of the bandwidth. In this article, we propose a method for automatic selection of the bandwidth that minimizes the asymptotic mean square error. Then, the estimated bandwidth by the proposed method is compared with the theoretical optimal bandwidth and a bandwidth by plug-in method. Simulation study is performed and shows satisfactory behavior of the proposed method.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.27-32
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• 2000

To overcome boundary problems with wavelet regression, we propose a simple method that reduces bias at the boundaries. It is based on a combination of wavelet functions and low-order polynomials. The utility of the method is illustrated with simulation studies and a real example. Asymptotic results show that the estimators are competitive with other nonparametric procedures.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.2
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• pp.1-7
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• 1992

The computational methods of extreme sea level are developed in this study. Based on type III asymptotic distribution, non-linear multiple regression method, skewness method and maximum likelihood method are used to evaluate the parameters of the distribution. The difference between real data and evaluated distribution function is fitted to get more desirable accuracy by employing polynominals. The numerical examples are given in the last section in order to illustrate the application of the present scheme.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.205-216
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• 1996

The bootstrap calibration method for empirical likelihood is considered to make a confidence region for the regression coefficients. Asymptotic properties are studied regarding the coverage probability. Small sample simulation results reveal that the bootstrap calibration works quite well.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.193-211
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• 2012

This paper deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we consider $Z_i=(X_i,Y_i)$, $i{\in}\mathbb{N}^N$ be a $\mathcal{F}{\times}\mathbb{R}$-valued measurable strictly stationary spatial process, where $\mathcal{F}$ is a semi-metric space and we study the spatial interaction of $X_i$ and $Y_i$ via the robust estimation for the regression function. We propose a family of robust nonparametric estimators for regression function based on the kernel method. The main result of this work is the establishment of the asymptotic normality of these estimators, under some general mixing and small ball probability conditions.