The shooting S-estimator for robust regression

Öllerer, Viktoria; Alfons, Andreas; Croux, Christophe

doi:10.1007/s00180-015-0593-7

Cited by 25 publications

(6 citation statements)

References 15 publications

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“…where Σ XX and Σ XY are the components of the empirical covariance matrix, and µ Y and µ X are empirical means of Y and X, respectively. As suggested by a number of authors [8,[23][24][25][26][27][28], the components of the solution stated in Equation ( 10) can be robustified to immunize the estimator against case-wise and cell-wise outliers. Inspired by [9], we use a modified version of the GRE algorithm to obtain robust estimates of means and covariances needed in the solution presented in Equation (10).…”

Section: The Proposed Estimatormentioning

confidence: 99%

“…A number of authors [8,[23][24][25][26][27][28] have proposed robust regression models that are resilient to case-wise and cell-wise outliers by robustifying the components of the covariance matrix in the solution of the least square (LS) optimization problem. Additionally, the multivariate S-estimator is incorporated instead of the empirical covariance and mean [24,25].…”

Section: Introductionmentioning

confidence: 99%

“…The EMVE estimator can be considered to be an initial value and a generalization of the minimum volume ellipsoid (MVE) estimator proposed in [15]. Moreover, the shooting S-estimator that is derived in [28] assigns individual weights to each cell in the data table, combining the shooting algorithm [29] and the simple S-regression [19]. Observe that the data may be snipped replacing cell-wise outliers by missing values NA [27].…”

Section: Introductionmentioning

confidence: 99%

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Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

et al. 2020

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Both cell-wise and case-wise outliers may appear in a real data set at the same time. Few methods have been developed in order to deal with both types of outliers when formulating a regression model. In this work, a robust estimator is proposed based on a three-step method named 3S-regression, which uses the comedian as a highly robust scatter estimate. An intensive simulation study is conducted in order to evaluate the performance of the proposed comedian 3S-regression estimator in the presence of cell-wise and case-wise outliers. In addition, a comparison of this estimator with recently developed robust methods is carried out. The proposed method is also extended to the model with continuous and dummy covariates. Finally, a real data set is analyzed for illustration in order to show potential applications.

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Section: The Proposed Estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

et al. 2020

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“…To evaluate the OCD Lasso estimator, we conduct MonteCarlo experiments with a setup similar to [16], which is one of the few papers that consider the ICM. As benchmark comparison we consider the classical OLS Lasso [2], MM Lasso [8], and adaptive MM Lasso [8].…”

Section: Simulationsmentioning

confidence: 99%

The outlier-corrected-data-adaptive Lasso: A new robust estimator for the independent contamination model

Machkour

Alt

Muma

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Many of today's signal processing tasks consider sparse models where the number of explanatory variables exceeds the sample size. When dealing with real-world data, the presence of impulsive noise and outliers must also be accounted for. Accurate and robust parameter estimation and consistent variable selection are needed simultaneously. Recently, some popular robust methods have been adapted to such complex settings. Especially, in high dimensional settings, however, it is possible to have a single contaminated predictor being responsible for many outliers. The amount of outliers introduced by this predictor easily exceeds the breakdown point of any existing robust estimator. Therefore, we propose a new robust and sparse estimator, the Outlier-Corrected-Data-(Adaptive) Lasso (OCD-(A) Lasso). It simultaneously handles highly contaminated predictors in the dataset and performs well under the classical contamination model. In a numerical study, it outperforms competing Lasso estimators, at a largely reduced computational complexity compared to its robust counterparts.

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“…In order to handle cellwise contamination, some new robust procedures have been proposed in the context of low‐dimensional multivariate location and scatter estimation, linear models, linear mixed models, and cluster analysis . Robust estimation of sparse covariance and inverse covariance matrices via pairwise estimates have been recently studied in by Tarr et al, Oellerer and Croux, and Han et al Refer to the latter paper for an account of rank based high‐dimensional covariance matrix estimation.…”

Section: High‐dimensional Statisticsmentioning

confidence: 99%

Robust statistics: a selective overview and new directions

Medina

Ronchetti

2015

WIREs Computational Stats

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Classical statistics relies largely on parametric models. Typically, assumptions are made on the structural and the stochastic parts of the model and optimal procedures are derived under these assumptions. Standard examples are least squares estimators in linear models and their extensions, maximum-likelihood estimators and the corresponding likelihood-based tests, and generalized methods of moments (GMM) techniques in econometrics. Robust statistics deals with deviations from the stochastic assumptions and their dangers for classical estimators and tests and develops statistical procedures that are still reliable and reasonably efficient in the presence of such deviations. It can be viewed as a statistical theory dealing with approximate parametric models by providing a reasonable compromise between the rigidity of a strict parametric approach and the potential difficulties of interpretation of a fully nonparametric analysis. Many classical procedures are well known for not being robust. These procedures are optimal when the assumed model holds exactly, but they are biased and/or inefficient when small deviations from the model are present. The statistical results obtained from standard classical procedures on real data applications can therefore be misleading. In this paper we will give a brief introduction to robust statistics by reviewing some basic general concepts and tools and by showing how they can be used in data analysis to provide an alternative complementary analysis with additional useful information. In this study, we focus on robust statistical procedures based on M-estimators and tests because they provide a unified statistical framework that complements the classical theory. Robust procedures will be discussed for standard models, including linear models, general linear model, and multivariate analysis. Some recent developments in high-dimensional statistics will also be outlined.

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The shooting S-estimator for robust regression

Cited by 25 publications

References 15 publications

Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

The outlier-corrected-data-adaptive Lasso: A new robust estimator for the independent contamination model

Robust statistics: a selective overview and new directions

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