Minimum Sum Of Absolute Errors Research Articles

Moth flame-random search optimization of a zero-dimensional model of a proton exchange membrane fuel cell

Modelling of proton exchange membrane fuel cell (PEMFC) is important for better understanding, simulation, and design of high-efficiency fuel cell systems. PEMFC models are often multivariate with several nonlinear elements. Metaheuristic algorithms that are successful in solving nonlinear optimization problems are good candidates for this purpose. This study proposes a new metaheuristic algorithm called MFORS that uses the advantages of the moth-flame optimization algorithm in global search and the non-deterministic properties of the random search algorithm to identify the optimal parameters of the PEMFC model. The sum of squared errors between the estimated and measured voltage is a quality of fit criterion. To show the effectiveness of the proposed algorithm, two case studies of zero-dimensional models of SR-12 Modular PEM Generator and Ballard Mark V fuel cell are considered. The sum of squared errors for the parameter estimated of electrical PEMFCs by the proposed MFORS algorithm is compared with recent works. The results showed that by the MFORS algorithm, the minimum sum of absolute errors of the actual stack voltage and the simulated stack voltage in the two PEMFC are 0.095037 and 0.018019, compared with the second-best algorithm results giving 0.09681 and 0.8092, respectively.

Restringindo flexibilidade de pesos em DEA utilizando análise de regressão MSEA

Este artigo apresenta um procedimento baseado no uso de regressão de mínima soma dos valores absolutos dos resíduos (MSAE) para o tratamento dos pesos dos fatores na Análise de Envoltória de Dados (DEA). É desenvolvido um método alternativo para limitar a faixa em que se permite que esses pesos possam variar, no caso de modelos contendo apenas um output.

Influence measure for the L1 regression

Because outliers and leverage observations unduly affect the least squares regression, the identification of influential observations is considered an important and integrai part of the analysis. However, very few techniques have been developed for the residual analysis and diagnostics for the minimum sum of absolute errors, L1 regression. Although the L1 regression is more resistant to the outliers than the least squares regression, it appears that outliers (leverage) in the predictor variables may affect it. In this paper, our objective is to develop an influence measure for the L1 regression based on the likelihood displacement function. We illustrate the proposed influence measure with examples.

Multivariate multiple linear regression based on the minimum sum of absolute errors criterion

We propose the minimum sum of absolute errors (MSAE) criterion for estimating the unknown parameters of a multivariate multiple linear regression model. It is less sensitive to outliers than the popular least squares procedure. A multivariate multiple linear regression problem may be viewed as a multiple criteria decision problem. Using the MSAE criterion the estimation problem can be formulated and solved as a multiple objective linear programming problem. We illustrate the idea with a bicriteria example.

Bootstrap confidence intervals for the minimum sum of absolute errors regression∗

At present very little is known about inference procedures on the parameters of the minimum sum of absolute errors, MSAE, regression model for small to medium size samples. We propose the use of bootstrap methods for this purpose. The (1 - α) confidence intervals on the parameters of the regression model may be constructed by using the bootstrap standard deviation or the bootstrap sampling distribution of the MSAE estimator. We compare and contrast the performance and quality of the intervals obtained by the two methods via a Monte Carlo study.

Intervals which Leave the Minimum Sum of Absolute Errors Regression Unchanged

One of the appealing properties of the minimum sum of absolute errors (MSAE) regression is its resistance to outliers and long-tailed error distributions. Just like the sample median, the MSAE estimators are influenced by all the observations but determined by only a subset of the observations. The MSAE estimates are not altered if the value of the response (or predictor) variable for an observation associated with a non-O residual is within a certain interval. In this paper we develop procedures to determine such intervals for the simple linear regression model

An algorithm for the MSAE estimation of the multistage dose-response model

The least squares procedure is often used to estimate the parameters of the multistage dose-response model. However. these estimates are unduly affected by outliers in a data set. The minimum sum of absolute errors. MSAE estimates are more resistant to outliers than the least squares estimates. Algorithms to compute the MSAE estimates can be tedious and computationally burdensome. We propose a linear approximation for the dose-response model that can be used to find the MSAE estimates by a simple and computationally less intensive algorithm. A few illustrative examples show that we get comparable values of the MSAE estimates of the parameters in a dose-response model using the exact model and the linear approximation.

An iterative procedure for the estimation of parameters in a dose-response model

The least squares estimates of the parameters in the multistage dose-response model are unduly affected by outliers in a data set whereas the minimum sum of absolute errors, MSAE estimates are more resistant to outliers. Algorithms to compute the MSAE estimates can be tedious and computationally burdensome. We propose a linear approximation for the dose-response model that can be used to find the MSAE estimates by a simple and computationally less intensive algorithm. A few illustrative ex-amples and a Monte Carlo study show that we get comparable values of the MSAE estimates of the parameters in a dose-response model using the exact model and the linear approximation.

Perturbation analysis for the minimum sum of absolute errors regression

In this paper we study the effect of independent and simultaneous changes in the values of the response variable for all the observations on the minimum sum of absolute errors (or for brevity absolute errors) regression. We develop an algorithm to determine the maximum amount by which the values of the response variable can change without changing the absolute errors regression hyperplane. We illustrate the results with an example.

An Efficient Algorithm for the MSAE and the MMAE Regression Problems

In the past quarter century, the minimum sum of absolute errors (MSAE) regression and the minimization of the maximum absolute error (MMAE) regression have attracted much attention as alternatives to the popular least squares regression. For the multiple linear regression, the MSAE and the MMAE regression problems can be formulated and solved as linear programming problems. Several efficient special purpose algorithms have been developed for each problem. Thus one needs two different algorithms and two separate computer codes to find the MSAE and the MMAE regression equations. In this paper, we develop an efficient algorithm to solve both problems. The proposed algorithm exploits the special structure of and the similarities between the problems. We illustrate it with a simple numerical example.

Transformations and Influential Observations in Minimum Sum of Absolute Errors Regression

The Box-Cox power transformation model is considered for minimum sum of absolute errors (MSAE) regression. A long-tailed error distribution, specifically the Laplace distribution, is included and could accommodate observations that in the normal case are outlying or unduly influencing a choice of transformation. The log-likelihood procedure of Box and Cox (1964) for obtaining the optimal transformation parameter is adapted for Laplace errors and MSAE regression. Graphical methods for detecting the influence of individual observations on the choice of transformation are described. Application to examples illustrates that this approach can provide valuable additional information to the data analyst.

Transformations and Influential Observations in Minimum Sum of Absolute Errors Regression

The Box-Cox power transformation model is considered for minimum sum of absolute errors (MSAE) regression. A long-tailed error distribution, specifically the Laplace distribution, is included and could accommodate observations that in the normal case are outlying or unduly influencing a choice of transformation. The log-likelihood procedure of Box and Cox (1964) for obtaining the optimal transformation parameter is adapted for Laplace errors and MSAE regression. Graphical methods for detecting the influence of individual observations on the choice of transformation are described. Application to examples illustrates that this approach can provide valuable additional information to the data analyst.

Remark AS R68: Constrained and Unconstrained L 1 Estimation A Remark on AS108: Multiple Linear Regression with Minimum Sum of Absolute Errors

Remark AS R68: Constrained and Unconstrained L 1 Estimation A Remark on AS108: Multiple Linear Regression with Minimum Sum of Absolute Errors

Interior Analysis for the Minimum Sum of Absolute Errors Regression

In this article we study the effect of each observation in a data set on the minimum sum of absolute errors (MSAE) regression. First, we study the extent to which the value of a response variable for an observation can be changed without affecting the MSAE regression fit and then show that MSAE regression is less sensitive to certain types of discrepant observations. Second, we study the effect of deleting an observation on parameter estimation. We illustrate the analysis with examples.

Algorithm AS 108: Multiple Linear Regression with Minimum Sum of Absolute Errors

Algorithm AS 108: Multiple Linear Regression with Minimum Sum of Absolute Errors