• The Korean Journal of Applied Statistics
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• v.21 no.4
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• pp.561-569
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• 2008

In this paper, we propose the double robust estimators which are the solutions of the double robust estimating equations to analyze and treat the outliers in the stock market data in Korea including the IMF period. The feasibility study shows that the proposed estimators work quitely better than the least squares estimators and the conventional robust estimators.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.517-525
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• 2011

This paper shows the performance evaluation of a robust estimator based on the GARCH model. We first introduce the method of a robust estimate in the GARCH model and the method of an outlier detection in the GARCH model. The results of the real internet traffic data show the out-performance of the robust estimator over the outlier detection method in the GARCH model. In addition, the method of the robust estimate is less complex than the method of the outlier detection method in the GARCH model.

• Journal of the Korean Data and Information Science Society
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• v.11 no.1
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• pp.1-18
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• 2000

In this paper, we study several parameter estimation methods used for autoregressive processes and compare them in view of forecasting. The least square estimation, least absolute deviation estimation, robust estimation are compared through Monte Carlo simulations.

• Journal of the Korean Geophysical Society
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• v.5 no.2
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• pp.131-142
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• 2002

Geomagnetic transfer function is generally estimated by choosing transfer to minimize the square sum of differences between observed values. If the error structure sccords to the Gaussian distribution, standard least square(LS) can be the estimation. However, for non-Gaussian error distribution, the LS estimation can be severely biased and distorted. In this paper, the Gaussian error assumption was tested by Q-Q(Quantile-Quantile) plot which provided information of real error structure. Therefore, robust estimation such as regression M-estimate that does not allow a few bad points to dominate the estimate was applied for error structure with non-Gaussian distribution. The results indicate that the performance of robust estimation is similar to the one of LS estimation for Gaussian error distribution, whereas the robust estimation yields more reliable and smooth transfer function estimates than standard LS for non-Gaussian error distribution.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.475-488
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• 2004

Several robust regression estimators are compared under contamination. Symmetric and asymmetric contamination schemes are used to measure the variance and MSE of regression estimators. Under asymmetric contamination depth-based regression estimator, especially projection based regression estimator(rcent) outperforms the rest and under symmetric contamination HBR performs relatively well.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.541-550
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• 2010

The $L_1$-regression estimator is susceptible to the leverage points, even though it is highly robust to the vertical outliers. This article is concerned with the improvement of robustness of the $L_1$-estimator. To improve its robustness, in terms of the breakdown point, we attempt to dampen the influence of the leverage points by means of reducing the weights corresponding to the leverage points. In addition the algorithm employs the linear scaling transformation technique, for higher computational efficiency with the large data sets, to solve the linear programming problem of $L_1$-estimation. Monte Carlo simulation results indicate that the proposed algorithm yields $L_1$-estimates which are robust to the leverage points as well as the vertical outliers.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.97-110
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• 2006

Since it is well-established that even high quality data tend to contain outliers, one would expect fat? greater reliance on robust regression techniques than is actually observed. But most of all robust regression estimators suffers from the computational difficulties and the lower efficiency than the least squares under the normal error model. The weighted self-tuning estimator (WSTE) recently suggested by Lee (2004) has no more computational difficulty and it has the asymptotic normality and the high break-down point simultaneously. Although it has better properties than the other robust estimators, WSTE does not have full efficiency under the normal error model through the weighted least squares which is widely used. This paper introduces a new approach as called the reweighted WSTE (RWSTE), whose scale estimator is adaptively estimated by the self-tuning constant. A Monte Carlo study shows that new approach has better behavior than the general weighted least squares method under the normal model and the large data.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.761-770
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• 2011

Robust principal components regression is suggested to deal with both the multicollinearity and outlier problem. A main aspect of the robust principal components regression is the selection of an optimal set of principal components. Instead of the eigenvalue of the sample covariance matrix, a selection criterion is developed based on the condition index of the minimum volume ellipsoid estimator which is highly robust against leverage points. In addition, the least trimmed squares estimation is employed to cope with regression outliers. Monte Carlo simulation results indicate that the proposed criterion is superior to existing ones.

• The Korean Journal of Applied Statistics
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• v.20 no.3
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• pp.551-559
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• 2007

The maximum likelihood estimation is not robust against outliers in the logistic regression. Thus we propose an algorithm for the robust estimation, which identifies the bad leverage points and vertical outliers by the V-mask type criterion, and then strives to dampen the effect of outliers. Our main finding is that, by an appropriate selection of weights and factors, we could obtain the logistic estimates with high breakdown point. The proposed algorithm is evaluated by means of the correct classification rate on the basis of real-life and artificial data sets. The results indicate that the proposed algorithm is superior to the maximum likelihood estimation in terms of the classification.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.471-485
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• 2016

Least squares (LS) regression is a classic method for regression that is optimal under assumptions of regression and usual observations. However, the presence of unusual data in the LS method leads to seriously distorted estimates. Therefore, various robust estimation methods are proposed to circumvent the limitations of traditional LS regression. Among these, there are M-estimators based on maximum likelihood estimation (MLE), L-estimators based on linear combinations of order statistics and R-estimators based on a linear combinations of the ordered residuals. In this paper, robust regression estimators with high breakdown point and/or with high efficiency are compared under several simulated situations. The paper analyses and compares distributions of estimates as well as relative efficiencies calculated from mean squared errors (MSE) in the simulation study. We conclude that MM-estimators or GR-estimators are a good choice for the real data application.