The Shooting S-Estimator for Robust Regression

Oellerer, Viktoria; Alfons, Andreas; Croux, Christophe

doi:10.2139/ssrn.2381960

Cited by 9 publications

(13 citation statements)

References 17 publications

(6 reference statements)

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“…Methods assuming a cellwise contamination are, however, still not that well investigated. For example, in a regression setting assuming n > p, MM regression was considered in Filzmoser, Höppner, Ortner, Serneels, and Verdonck (2020), a three step procedure based on S-estimators in Leung, Zhang, and Zamar (2016) shooting S-estimator in Öllerer, Alfons, and Croux (2016), combining ideas from simple S-regression with the 'shooting algorithm', which is a coordinate descent algorithm. The shooting S-estimator was recently extended to the high-dimensional setting in Bottmer, Croux, and Wilms (2020).…”

Section: Cellwise Contaminationmentioning

confidence: 99%

Robust linear regression for high‐dimensional data: An overview

Filzmoser

Nordhausen²

2020

WIREs Computational Stats

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Digitization as the process of converting information into numbers leads to bigger and more complex data sets, bigger also with respect to the number of measured variables. This makes it harder or impossible for the practitioner to identify outliers or observations that are inconsistent with an underlying model. Classical least-squares based procedures can be affected by those outliers. In the regression context, this means that the parameter estimates are biased, with consequences on the validity of the statistical inference, on regression diagnostics, and on the prediction accuracy. Robust regression methods aim at assigning appropriate weights to observations that deviate from the model. While robust regression techniques are widely known in the lowdimensional case, researchers and practitioners might still not be very familiar with developments in this direction for high-dimensional data. Recently, different strategies have been proposed for robust regression in the high-dimensional case, typically based on dimension reduction, on shrinkage, including sparsity, and on combinations of such techniques. A very recent concept is downweighting single cells of the data matrix rather than complete observations, with the goal to make better use of the model-consistent information, and thus to achieve higher efficiency of the parameter estimates. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical and Graphical Methods of Data Analysis > Dimension Reduction

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Section: Cellwise Contaminationmentioning

confidence: 99%

Robust linear regression for high‐dimensional data: An overview

Filzmoser

Nordhausen²

2020

WIREs Computational Stats

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“…Then, the cell-rPLR method was applied as described in Section 2. The resulting heatmap is shown in Figure 3 using the adjusted Tukey biweight function (8) and in Figure 4, which is based on the adjusted Hampel function (12). For reasons of space, we omitted the first 36 control patients from the visualization and showed only controls 37 to 50 and the patients from the different disease groups, separated by black horizontal lines.…”

Section: Visualization Of Cellwise Outliersmentioning

confidence: 99%

“…Cellwise outlier detection is a quite recent topic in robust statistics, 7 as well as the development of robust estimators with cellwise outliers. 8 In fact, since our proposed algorithm will be based on variable pairs, there is some similarity to the algorithm of Rousseeuw and Bossche. 7 Data from metabolomics often have big differences in abundance of individually measured variables.…”

mentioning

confidence: 99%

Cellwise outlier detection and biomarker identification in metabolomics based on pairwise log ratios

Walach

Filzmoser

Kouřil

et al. 2019

Journal of Chemometrics

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Data outliers can carry very valuable information and might be most informative for the interpretation. Nevertheless, they are often neglected. An algorithm called cellwise outlier diagnostics using robust pairwise log ratios (cell-rPLR) for the identification of outliers in single cell of a data matrix is proposed. The algorithm is designed for metabolomic data, where due to the size effect, the measured values are not directly comparable. Pairwise log ratios between the variable values form the elemental information for the algorithm, and the aggregation of appropriate outlyingness values results in outlyingness information. A further feature of cell-rPLR is that it is useful for biomarker identification, particularly in the presence of cellwise outliers. Real data examples and simulation studies underline the good performance of this algorithm in comparison with alternative methods.

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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 9 publications

References 17 publications

Robust linear regression for high‐dimensional data: An overview

Robust linear regression for high‐dimensional data: An overview

Cellwise outlier detection and biomarker identification in metabolomics based on pairwise log ratios

Robust statistics: a selective overview and new directions

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