An evolutionary algorithm for robust regression

Nunkesser, Robin; Morell, Oliver

doi:10.1016/j.csda.2010.04.017

Cited by 21 publications

(9 citation statements)

References 18 publications

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“…Robust estimators for linear regression models including repeated median (RM) (Siegel, 1982), least median of squares (LMS) and the least trimmed squares (LTS) (Rousseeuw, 1984), S-estimate (Rousseeuw and Yohai, 1984), Fast-LTS (Rousseeuw and Driessen, 2006), efficient computation by Flores (2010), and evolutionary algorithm proposed by Nunkesser and Morell (2010) are introduced. All of them have very low efficiency for a regression model under normality assumption.…”

Section: τ −Estimate and Fast −τ −Estimatementioning

confidence: 99%

Parameter Estimation of Autoregressive Models Using the Iteratively Robust Filtered Fast-τ Method

Fokalaei¹,

Shahriari

Shafaei

2014

Communications in Statistics - Theory and Methods

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Utilizing time series modeling entails estimating the model parameters and dispersion. Classical estimators for autocorrelated observations are sensitive to presence of different types of outliers and lead to bias estimation and misinterpretation. It is important to present robust methods for parameters estimation which are not influenced by contaminations. In this article, an estimation method entitled Iteratively Robust Filtered Fast−τ (IRFFT) is proposed for general autoregressive models.In comparison to other commonly accepted methods, this method is more efficient and has lower sensitivity to contaminations due to having desirable robustness properties. This has been demonstrated by applying MSE, influence function, and breakdown point criteria.

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Section: τ −Estimate and Fast −τ −Estimatementioning

confidence: 99%

Parameter Estimation of Autoregressive Models Using the Iteratively Robust Filtered Fast-τ Method

Fokalaei¹,

Shahriari

Shafaei

2014

Communications in Statistics - Theory and Methods

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“…Since, median is not a continuous function of squared residuals, gradient based optimization techniques are not applicable. Therefore, several algorithms were developed for the LMS in Winker et al (2011), Nunkesser andMorell (2010) and Karr et al (1995) among others.…”

Section: Preliminariesmentioning

confidence: 99%

A New Algorithm for Detecting Outliers in Linear Regression

Satman¹

2013

IJSP

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In this paper, we present a new algorithm for detecting multiple outliers in linear regression. The algorithm is based on a non-iterative robust covariance matrix and concentration steps used in LTS estimation. A robust covariance matrix is constructed to calculate Mahalanobis distances of independent variables which are then used as weights in weighted least squares estimation. A few concentration steps are then performed using the observations that have smallest residuals. We generate random data sets for n = 10 3 , 10 4 , 10 5 and p = 5, 10 to show up the capabilities of the algorithm. In our Monte Carlo simulations, it is shown that our algorithm has very low masking and swamping ratios when the number of observations is up to 10 4 in the case of maximum contamination in X-Space. It is also shown that, the algorithm is successful in the case of Y-Space outliers when the contamination level, sample size and number of parameters are up to 30%, n = 10 5 , and p = 10, respectively. Bias, variance and MSE statistics are calculated for different scenarios. The reported computation time of our implementation is quite short. It is concluded that the presented algorithm is suitable and applicable for detecting multiple outliers in regression analysis with its small masking and swamping ratios, accurate estimates of regression parameters except the intercept, and short computation time in large data sets and high level of contamination. A future work is required for reducing bias and variance of the intercept estimator in the model.

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“…It is the basis of fast heuristic algorithms in high-breakdown regression [50]. Several recent methods based on this formulation, including evolutionary and semidefinite programming, were presented in [3,4,9,36,37,53]. The four methods mentioned above achieve the highest attainable asymptotic breakdown point of 1/2, which means that up to a half of the data can be contaminated without affecting the estimator.…”

Section: Optimizationmentioning

confidence: 99%

Derivative-free optimization and neural networks for robust regression

Beliakov¹,

Kelarev²,

Yearwood³

2012

Optimization

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Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks to contaminated data using least trimmed squares criterion. We introduce a penalized least trimmed squares criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression.

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An evolutionary algorithm for robust regression

Cited by 21 publications

References 18 publications

Parameter Estimation of Autoregressive Models Using the Iteratively Robust Filtered Fast-τ Method

Parameter Estimation of Autoregressive Models Using the Iteratively Robust Filtered Fast-τ Method

A New Algorithm for Detecting Outliers in Linear Regression

Derivative-free optimization and neural networks for robust regression

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