• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.733-739
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• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.

• 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 Statistical Society
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• v.26 no.3
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• pp.383-395
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• 1997

This paper proves that the standard bootstrap approximation for the least absolute deviation (LAD) estimate of .beta. in AR(1) processes with infinite variance error terms is asymptotically valid in probability when the bootstrap resample size is much smaller than the original sample size. The theoretical validity results are supported by simulation studies.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1235-1243
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• 2010

This study proposes a trimmed LAD(least absolute deviation) estimators for multi-dimensional contingency tables and suggests an algorithm to estimate it. In addition, a method to determine the trimming quantity of the estimators is suggested. A Monte Carlo study shows that the propose method yields a better trimming rate and coverage rate than the previously suggest method based on the determinant of the covariance matrix.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.349-358
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• 1998

Consider the AR(1) model $X_{t}$=$\beta$ $X_{t-1}$+$\varepsilon$$_{t}$ where $\beta$ < 1 is an unknown parameter to be estimated and {$\varepsilon$$_{t}$} denotes the independent and identically distributed error terms with unknown common distribution function F. In this paper, a strong representation for the least absolute deviation (LAD) estimate of $\beta$ in AR(1) models is obtained under some mild conditions on F. on F.F.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.288-295
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• 1995

In this paper a hypotheses test procedure based on the least absolute deviation estimators for the unknown parameters in nonlinear regression models is investigated. The asymptotic distribution of the proposed likelihood ratio test statistic are established voth under the null hypotheses and a sequence of local alternative hypotheses. The asymptotic relative efficiency of the proposed test with classical test based on the least squares estimator is also discussed.

• 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.