On the Robustness of Absolute Deviations with Fuzzy Data
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Least absolute deviations
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This paper introduces a least absolute deviation method for system identification.An iterative algorithm for the linear least absolute deviation regression coefficients is given.Comparison with the Least square method,this algorithm is more robust.Simulation results are also given.
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ARIYANTO HERMAWAN. Parameter Estimation of Dynamical Model using Robust Median Absolute Deviation (MAD) and Huber M-Estimation Methods. Supervised by NGAKAN KOMANG KUTHA ARDANA and ALI KUSNANTO. Parameter estimation is commonly applied to regression models. However, the estimation of the dynamic models have not been developed. Least Square Method is the most common method used in parameter estimation. However, this method is not appropriate to be used if data contains some outliers. Robust method is a method that can overcome the weakness of the Least Square method. Median Absolute Deviation and M-Estimation are some suitable methods used when the data contains outliers and far outliers. Both of these robust methods are quite good in parameter estimation for the data with or without outliers. Based on Symmetrical Mean Absolute Percentage Error (SMAPE) and boxplot, MEstimation method has better accuracy in parameter estimation than the Median Absolute Deviation method. In this manuscript, parameter estimation is applied to Gompertz and SZR (Susceptible, Zombie, Removed) model using hypothetical data.
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The method of least absolute deviation provides a robust alternative to least squares, particularly when the data follow distributions that are non-normal and subject to outliers. While inference in least squares estimation is well understood, inferential procedures in the situation of least absolute deviation estimation have not been studied as extensively, particularly in the presence of autocorrelation. In this search, we study two alternative significance test procedures in least absolute deviation regression, along with two approaches used to correct for serial correlation. The study is based on a Monte Carlo simulation, and comparisons are made based on observed significance levels.
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The least absolute deviation criteria is widely used in engineering because of its robustness, but the algorithms for solving the least absolute deviation estimate of the regression coefficient are too explicated or only efficient for small sample points and variables. In this paper, a new method based on simulated annealing algorithm to solve the least absolute deviation estimates of regression coefficient is presented by changing the problem to the combinatorial optimization based on it's properties. At last the numerical experimentations verified the validity of the new method.
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Abstract A brief review and bibliography of least absolute values (LAV) estimation is given. This paper serves to introduce the other articles in this special issue on the computational aspects of LAV estimation. Keywords: least absolute deviations estimationminimum sum of absolute errorsminimum absolute deviationslinear programming
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In a recent educational technical note in SIGMAP, [3], Swanson and Woolsey outlined how one can determine the unknown parameters of a linear model under the criterion of minimizing the sum of absolute deviations. This note will demonstrate that one can also use linear programming procedures under the criterion of minimizing the maximum absolute deviation. This transformation to a linear programming problem is known, but not of wide extent; and is useful when one is trying to identify "outliers".
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This paper first introduced least square method least absolute deviation and total least absolute deviation,discussed their similarities and differences;then illustrated the application of economic aspect on total least absolute deviation,made a comparison for least square method,least absolute deviation and total least absolute deviation,and used LINGO10 procedure calculate total least absolute deviation;finally,a brief description for total least absolute deviation in the further development of theory was given.
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The least absolute deviations are using widely used in engineering because of it's robustness,but the algorithm solving the least absolute deviation is not efficient. Changing the least absolute deviation to the combinatorial optimization,based on it's characters, we use the genetic algorithm to solve the least absolute deviation regression. At last the numerical experimentations show that the Genetic algorithm is efficient.
Least absolute deviations
Absolute deviation
Absolute (philosophy)
Robustness
Mean absolute error
Relative standard deviation
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Absolute (philosophy)
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Least absolute deviations
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Linear least squares forecasting is used on two data sets and these resulting equations are compared, along with their larger total absolute deviations, to regular least absolute deviation (LAD) equation fits done with multi stage Monte Carlo optimization (MSMCO). Then two nonlinear models are fitted using LAD with MSMCO. One is a regular LAD fit and the other uses mini max LAD curve fitting.
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