• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.649-656
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• 2005

In this paper we consider a fuzzy least absolute deviation method in order to construct fuzzy linear regression model with fuzzy input and fuzzy output. We also consider two numerical examples to evaluate an effectiveness of the fuzzy least absolute deviation method and the fuzzy least squares method.

• Journal of the Korean Statistical Society
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• 제29권2호
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• pp.187-199
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• 2000

In this paper, we deal with the asymptotic properties of the least absolute deviation estimators in the nonlinear time series regression model. For the sinusodial model which frequently appears in a time series analysis, we study the strong consistency and asymptotic normality of least absolute deviation estimators. And using the derived limiting distributions we show that the least absolute deviation estimators is more efficient than the least squared estimators when the error distribution of the model has heavy tails.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.127-139
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• 1995

This paper is concerned with the asymptotic properties of the least absolute deviation estimators for nonlinear regression models. The simple and practical sufficient conditions for the strong consistency and the asymptotic normality of the least absolute deviation estimators are given. It is confirmed that the extension of these properties to wide class of regression functions can be established by imposing some condition on the input values. A confidence region based on the least absolute deviation estimators is proposed and some desirable asymptotic properties including the asymptotic relative efficiency also discussed for various error distributions. Some examples are given to illustrate the application of main results.

• Communications for Statistical Applications and Methods
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• 제18권6호
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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.

• Communications for Statistical Applications and Methods
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• 제24권6호
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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.

• Communications for Statistical Applications and Methods
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• 제17권6호
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• pp.803-810
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• 2010

The singular value decomposition of a rectangular matrix is a basic tool to understand the structure of the data and particularly the relationship between row and column factors. However, conventional singular value decomposition used the least squares method and is not robust to outliers. We propose a simple robust singular value decomposition algorithm based on the weighted least absolute deviation which is not sensitive to leverage points. Its implementation is easy and the computation time is reasonably low. Numerical results give the data structure and the outlying information.

• Communications for Statistical Applications and Methods
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• 제30권2호
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• pp.135-147
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• 2023

Skipped median is more robust than median when outliers are not symmetrically distributed. In this work, we propose a novel algorithm to estimate the skipped median. The idea of skipped median and the new algorithm are extended to regression problem, which is called least clipped absolute deviation (LCAD). Since our proposed algorithm for nonconvex LCAD optimization makes use of convex least absolute deviation (LAD) procedure as a subroutine, regularizations developed for LAD can be directly applied, without modification, to LCAD as well. Numerical studies demonstrate that skipped median and LCAD are useful and outperform their counterparts, median and LAD, when outliers intervene asymmetrically. Some extensions of the idea for skipped median and LCAD are discussed.

• 산업경영시스템학회지
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• 제13권21호
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• pp.143-151
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• 1990

This paper studies a single machine scheduling problem in which all jobs have the common due date and penalties are assessed for jobs at different rates. The scheduling objective is to minimize the weighted mean absolute deviations(WMAD). This problem may provide greater flexibility in achieving scheduling objectives than the mean absolute deviation (MAD) problem. We propose three heuristic solution methods based on several dominance conditions. Numerical examples are presented. This article extends the results to the problem to the problem of scheduling n-jobs on m-parallel identical processors in order to minimize the weighted mean absolute deviation.

• Industrial Engineering and Management Systems
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• 제15권1호
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• pp.63-76
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• 2016

Multiperiod portfolio selection problem attracts more and more attentions because it is in accordance with the practical investment decision-making problem. However, the existing literature on this field is almost undertaken by regarding security returns as random variables in the framework of probability theory. Different from these works, we assume that security returns are uncertain variables which may be given by the experts, and take absolute deviation as a risk measure in the framework of uncertainty theory. In this paper, a new multiperiod mean absolute deviation uncertain portfolio selection models is presented by taking transaction costs, borrowing constraints and threshold constraints into account, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on uncertain theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. To solve the new model in general cases, the forward dynamic programming method is presented. In addition, a numerical example is also presented to illustrate the modeling idea and the effectiveness of the designed algorithm.

• 한국ITS학회 논문지
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• 제12권6호
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• pp.10-21
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• 2013

본 연구에서는 교통정보시스템에서 통행시간의 이상치 자료를 제거하기 위한 복합 필터링 모형을 제시하였으며, 이는 중위절대편차법과 Voting Rule을 기반으로 하는 이중화된 필터링 모형에 해당한다. 본 모형은 중위절대편차법을 이용해 표본을 정규분포화 시키기 위한 1차 필터링을 수행하며, 이후 Voting Rule을 이용해 중위절대편차법의 적용 이후에도 남아 있는 이상치 자료를 제거하는 방식에 해당한다. 이때 Voting Rule은 표본의 통행시간과 평균통행시간의 차이가 임계치를 초과하는 경우 해당 표본을 이상치로 판정하며, 다수결의 원칙을 이용하여 이상치 자료의 비율에 따라 이상치에 대한 제거 여부를 결정한다. 일반국도 3호선의 경기도 광주시 구간을 대상으로 한 사례분석을 통해 복합 필터링 모형이 이상치 표본 만을 선택적으로 제거하여 통행시간 추정의 정확도 개선에 기여할 수 있음을 확인하였다.