• 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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• 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.

• Wind and Structures
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• 제26권6호
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• pp.383-395
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• 2018

An accurate determination of wind speed distribution is the basis for an evaluation of the wind energy potential required to design a wind turbine, so it is important to estimate unknown parameters of wind speed distribution. In this paper, Gumbel distribution is used in modelling wind speed data, and alternative robust estimation methods to estimate its parameters are considered. The methodologies used to obtain the estimators of the parameters are least absolute deviation, weighted least absolute deviation, median/MAD and least median of squares. The performances of the estimators are compared with traditional estimation methods (i.e., maximum likelihood and least squares) according to bias, mean square deviation and total mean square deviation criteria using a Monte-Carlo simulation study for the data with and without outliers. The simulation results show that least median of squares and median/MAD estimators are more efficient than others for data with outliers in many cases. However, median/MAD estimator is not consistent for location parameter of Gumbel distribution in all cases. In real data application, it is firstly demonstrated that Gumbel distribution fits the daily mean wind speed data well and is also better one to model the data than Weibull distribution with respect to the root mean square error and coefficient of determination criteria. Next, the wind data modified by outliers is analysed to show the performance of the proposed estimators by using numerical and graphical methods.

• Journal of the Korean Data and Information Science Society
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• 제11권1호
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• pp.1-18
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• 2000

본 논문에서는 가장 많이 사용되는 시계열 모형중의 하나인 자기회귀모형에서 모수를 추정하는 방법으로 최소 절대 편차 추정법(least absolute deviation estimation)을 포함한 로버스트한 추정방법 (robust estimation)의 사용을 제안하고 모의 실험을 통하여 이러한 방법들을 기존의 최소 제곱 추정 방법과 예측의 관점에서 비교 검토하여 시계열 자료분석에서의 로버스트한 모수 추정 방법의 유효성을 확인해 보고자 한다.

• 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.

• Journal of the Korean Statistical Society
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• 제27권1호
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• pp.101-112
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• 1998

This paper is concerned with the asymptotic properties of the least absolute deviation estimators for the nonlinear regression model when dependent variables are subject to censoring time, and proposed the simple and practical sufficient conditions for the strong consistency and asymptotic normality of the least absolute deviation estimators in censored regression model. Some desirable asymptotic properties including the asymptotic relative efficiency of proposed model with respect to standard model are given.