• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.273-293
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• 2019

We consider the problem of model selection in multiple linear regression with outliers and non-normal error distributions. In this article, the robust model selection criterion is proposed based on the robust estimation method with the least absolute deviation (LAD). The proposed criterion is shown to be consistent. We suggest proposed criterion based algorithms that are suitable for a large number of predictors in the model. These algorithms select only relevant predictor variables with probability one for large sample sizes. An exhaustive simulation study shows that the criterion performs well. However, the proposed criterion is applied to a real data set to examine its applicability. The simulation results show the proficiency of algorithms in the presence of outliers, non-normal distribution, and multicollinearity.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.673-683
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• 2017

The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.

• Economic and Environmental Geology
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• v.28 no.4
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• pp.433-438
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• 1995

The most popular minimization method is based on the least-squares criterion, which uses the $L_2$ norm to quantify the misfit between observed and synthetic data. The solution of the least-squares problem is the maximum likelihood point of a probability density containing data with Gaussian uncertainties. The distribution of errors in the geophysical data is, however, seldom Gaussian. Using the $L_2$ norm, large and sparsely distributed errors adversely affect the solution, and the estimated model parameters may even be completely unphysical. On the other hand, the least-absolute-deviation optimization, which is based on the $L_1$ norm, has much more robust statistical properties in the presence of noise. The solution of the $L_1$ problem is the maximum likelihood point of a probability density containing data with longer-tailed errors than the Gaussian distribution. Thus, the $L_1$ norm gives more reliable estimates when a small number of large errors contaminate the data. The effect of outliers is further reduced by M-fitting method with Cauchy error criterion, which can be performed by iteratively reweighted least-squares method.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.8
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• pp.1984-1989
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• 1998

Convergence properties of the stochastic gradient adaptive algorithm based on the least mean absolute third (LMAT) error criterion is presented.In particular, the performnce of the algorithmis examined and compared with least mena square (LMS) algorithm for several different probability densities of the measurement noisein a system identification mode. It is observedthat the LMAT algorithm outperforms the LMS algorithm for most of the noise probability densities, except for the case of the exponentially distributed noise.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.10
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• pp.2310-2316
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• 1997

This paper presents a comparative performance analysis of the stochastic gradient adaptive algorithm based on the least mean absolute third (LMAT) error criterion with other widely-used competing adaptive algorithms. Under the assumption that the signals involved are zero-mean, wide-sense stationary and Gaussian, approximate expressions that characterize the steady-state mean-squared estimation error of the algorithm is dervied. The validity of our derivation is then confirement by computer simulations. The convergence speed is compared under the condition that the LMAT and other competing algorithms converge to the same value for the mean-squared estimation error in the stead-state, and superior convergence property of the LMAT algorithm is observed. In particular, it is shown that the LMAT algorithm converges faster than other algorithms even through the eignevalue spread ratio of the input signal and measurement noise power change.

• The Journal of Industrial Distribution & Business
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• v.10 no.5
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• pp.7-20
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• 2019

Purpose - This study provides appropriate procedures for EFA to help researchers conduct empirical studies by using PLS-SEM. Research design, data, and methodology - This study addresses the absolute and relative sample size criteria, sampling adequacy, factor extraction models, factor rotation methods, the criterion for the number of factors to retain, interpretation of results, and reporting information. Results - The factor analysis procedure for PLS-SEM consists of the following five stages. First, it is important to look at whether both the Bartlett test of sphericity and the KMO MSA meet the qualitative criteria. Second, PAF is a better choice of methodology. Third, an oblique technique is a suitable method for PLS-SEM. Fourth, a combined approach is strongly recommended to factor retention. PA should be used at the onset. Next, it is recommended using the K1 criterion. In addition, it is necessary to extract factors that increase the total variance explanatory power through the PVA-FS. Finally, it is appropriate to select an item with a factor loading into 0.5 or higher and a communality of 0.5. Conclusions - It is expected that the accurate factor analysis processed for PLS-SEM as previously presented will help us extract more precise factors of the structural model.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.52 no.8
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• pp.450-456
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• 2003

This paper proposes a multiple time-series model with dummy variables for one-hour ahead load forecasting. We used 11 dummy variables that were classified by day characteristics such as day of the week, holiday, and special holiday. Also, model specification and selection of input variables including dummy variables were made by test statistics such as AIC(Akaike Information Criterion) and t-test statistics of each coefficient. OLS (Ordinary Least Squares) method was used for estimation and forecasting. We found out that model specifications for each hour are not identical usually at 30％ of optimal significance level, and dummy variables reduce the forecasting error if they are classified properly. The proposed model has much more accurate estimates in forecasting with less MAPE (Mean Absolute Percentage Error).

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.118-123
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• 2007

A robust objective function in the frequency domain is applied to the acoustic full waveform inversion. The proposed objective function is defined as $l_1$-norm of residual wavefields in the frequency domain. Generally, the full waveform inversion is extremely sensitive to a number of factors such as parameterization, initial model, noise and so on. The numerical tests were performed for checking the sensitivity to attenuation and several noises. For the comparison with other objective functions, the conventional least-squares method and the logarithmic method were tested under the same condition. The synthetic data examples show that the proposed algorithm is more robust than the well-known methods.

• Korean Journal of Veterinary Research
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• v.45 no.2
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• pp.239-244
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• 2005

Hematologic investigations were made on the blood samples taken from bovine leukemia virus (BLV)-seropositive Holstein-Friesian cattle in Korea, and their absolute lymphocyte count was compared with that of BLV-seronegative cattle. The incidence of persistent lymphocytosis (PL) was also determined. The normal bovine lymphocyte count was established on the basis of studies of 656 blood samples taken three times from 297 seronegative animals aged from 0~6 months to over 5 years at 5~6-month intervals. The data were examined according to 7 age groups of samples placed into their respective age groups. A peak in average total count was reached at 6~12 months ($5.36{\times}10^3/{\mu}l$) and thereafter the count declined continuously until over 5 years ($3.17{\times}10^3/{\mu}l$). From the results, 99.74 percent limits were calculated, and the upper limit of the range was chosen as the cutoff point for lymphocytosis. A PL was defined as a lymphocyte count that exceeded the above 99.74 percent limits and persisted over an interval of at least three months. The criterion for PL was applied to classifying 515 blood samples obtained four times from 189 seropositive animals without clinical signs at 5~7-month intervals. It was found that 54 (28.5%) of seropositive animals were with PL; cattle with PL were in age groups of 2~3 years to over 5 years.