• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.33-40
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• 1994

The conditional expectation of a random variable in a multivariate normal random vector is a multiple linear regression on its predecessors. Using this fact, the least median of squares estimation method developed in a multiple linear regression is adapted to a multivariate data to identify influential observations. The resulting method clearly detect outliers and it avoids the masking effect.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.269-279
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• 2002

We considered the problem for confirmation of multiple outliers and leverage points. Identification of multiple outliers and leverage points is difficult because of the masking effect and swamping effect. Rousseeuw and van Zomeren(1990) identified multiple outliers and leverage points by using the Least Median of Squares and Minimum Value of Ellipsoids which are high-breakdown robust estimators. But their methods tend to declare too many observations as extremes. Atkinson(1987) suggested a method for confirming of outliers and Fung(1993) pointed out Atkinson method's limitation and proposed another method by using the add-back model. But we analyzed that Fung's method is affected by adjacent effect. In this thesis, we proposed one procedure for confirmation of outliers and leverage points and compared three example with Fung's method.

• Korean Journal of Optics and Photonics
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• v.8 no.2
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• pp.88-94
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• 1997

Photographic lenses and an aspheric optical pickup-lens are designed by using damped least-squares(DLS) method. We start optimization with arbitrary initial damping factor. To improve the rate of convergence and the stability in optimization, we apply the special procedure that estimates numerical adequacy of derivative increments of variables to the DLS method. When the initial damping factor is almost equal to the median of series of eigenvalues, the convergence and the stability of the method significantly are improved. Optimized lenses have the performance of each target.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.485-494
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• 2004

An algorithm is proposed to identify multiple outliers in linear regression. It is based on the clustering of residuals from the least median of squares estimation. A cut-height criterion for the hierarchical cluster tree is suggested, which yields the optimal clustering of the regression outliers. Comparisons of the effectiveness of the procedures are performed on the basis of the classic data and artificial data sets, and it is shown that the proposed algorithm is superior to the one that is based on the least squares estimation. In particular, the algorithm deals very well with the masking and swamping effects while the other does not.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.291-304
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• 2002

This article is concerned with an effective algorithm for the identification of multiple outliers in linear regression. It proposes a hybrid algorithm which employs the least median of squares estimator, instead of the least squares estimator, to construct an Initial clean subset in the stepwise forward search scheme. The performance of the proposed algorithm is evaluated and compared with the existing competitor via an extensive Monte Carlo simulation. The algorithm appears to be superior to the competitor for the most of scenarios explored in the simulation study. Particularly it copes with the masking problem quite well. In addition, the orthogonal decomposition and Its updating techniques are considered to improve the computational efficiency and numerical stability of the algorithm.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.20 no.3
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• pp.500-506
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• 2019

In this study, we present a decision function of optimal smoothing parameter for baseline correction using Asymmetrically reweighted penalized least squares (arPLS). Baseline correction is very important due to influence on performance of spectral analysis in application of spectroscopy. Baseline is often estimated by parameter selection using visual inspection on analyte spectrum. It is a highly subjective procedure and can be tedious work especially with a large number of data. For these reasons, an objective procedure is necessary to determine optimal parameter value for baseline correction. The proposed function is defined by modeling the median value of possible parameter range as the length and order of the background signal. The median value increases as the length of the signal increases and decreases as the degree of the signal increases. The simulated data produced a total of 112 signals combined for the 7 lengths of the signal, adding analytic signals and linear and quadratic, cubic and 4th order curve baseline respectively. According to the experimental results using simulated data with linear, quadratic, cubic and 4th order curved baseline, and real Raman spectra, we confirmed that the proposed function can be effectively applied to optimal parameter selection for baseline correction using arPLS.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.149-157
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• 2004

The stationarity is one of the most important properties of a time series. We propose robust sign tests for seasonal autoregressive processes to determine whether or not a time series is stationary. The proposed tests are robust to the outliers and the heteroscedastic errors, and they have an exact binomial null distribution regardless of the period of seasonality and types of median adjustments. A Monte-Carlo simulation shows that the sign test is locally more powerful than the tests based on ordinary least squares estimator (OLSE) for heavy-tailed and/or heteroscedastic error distributions.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.349-360
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• 1995

This paper deals with the robustness properties of the minimum disparity estimation in linear regression models. The estimators defined as statistical quantities whcih minimize the blended weight Hellinger distance between a weighted kernel density estimator of the residuals and a smoothed model density of the residuals. It is shown that if the weights of the density estimator are appropriately chosen, the estimates of the regression parameters are robust.

• Journal of the Korea Society of Computer and Information
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• v.10 no.2 s.34
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• pp.21-30
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• 2005

In general, the robust estimation method is well known for a good statistical estimator that is insensitive to small departures from the idealized assumptions for which the estimation is optimized. While there are many existing robust estimation techniques that have been proposed in the literature, two main techniques used in computer vision are M-estimators and least-median of squares (LMS). Among these. we utilized the M-estimators since they are known to provide an optimal estimation of affine motion parameters. The M-estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized. To resolve these problems, we proposed an adaptive M-estimators algorithm that effectively separates outliers from non-outliers and estimate affine model parameters, using a continuous sigmoid weight function. The experimental results show the superiority of our method.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.7
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• pp.974-988
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• 1995

In this paper, we propose a range image segmentation algorithm using robust regression. We derive a least $\kappa$th-order square (LKS) method by generalizing the least median of squares (LMedS) method and compare it with the conventional robust regressions. The LKS is robuster against outliers than the LMedS and shows performance similar to the residual consensus (RESC). The RESC uses the predetermined number of sorted residuals, whereas the LKS uses an adaptive parameter determined by given observations rather than the a priori knowledge. Computer simulation with synthetic and real range images shows that the proposed LKS algorithm gives better performance than the conventional ones.