A Fast Algorithm for S-Regression Estimates

Salibián‐Barrera, Matías; Yohai, Vı́ctor J.

doi:10.1198/106186006x113629

Cited by 186 publications

(96 citation statements)

References 28 publications

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“…Robust also provides a default initial estimate with high breakdown point (not necessarily efficient), which is used in the first three algorithms in our experiments: when p = 15, it is the S-estimate computed via random resampling; when p = 50, it is the estimate from the fast PY procedure. Since it is well known that the initial estimate is outperformed by MM in terms of estimation efficiency and robustness, both theoretically and empirically (Yohai 1987;Salibian-Barrera & Yohai 2006;Peña & Yohai 1999 All methods apart from Θ-IPOD require a cutoff value to identify which residuals are outliers. We applied the fully efficient procedure which performas at least as well as the fixed choice of η = 2.5 in various situations (Gervini & Yohai 2002).…”

Section: Parameter Tuning In Outlier Detectionmentioning

confidence: 99%

Outlier Detection Using Nonconvex Penalized Regression

She

Owen

2011

Journal of the American Statistical Association

273

266

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This paper studies the outlier detection problem from the point of view of penalized regressions. Our regression model adds one mean shift parameter for each of the n data points. We then apply a regularization favoring a sparse vector of mean shift parameters. The usual L 1 penalty yields a convex criterion, but we find that it fails to deliver a robust estimator. The L 1 penalty corresponds to soft thresholding. We introduce a thresholding (denoted by Θ) based iterative procedure for outlier detection (Θ-IPOD). A version based on hard thresholding correctly identifies outliers on some hard test problems. We find that Θ-IPOD is much faster than iteratively reweighted least squares for large data because each iteration costs at most O(np) (and sometimes much less) avoiding an O(np 2 ) least squares estimate. We describe the connection between Θ-IPOD and M -estimators. Our proposed method has one tuning parameter with which to both identify outliers and estimate regression coefficients. A data-dependent choice can be made based on BIC. The tuned Θ-IPOD shows outstanding performance in identifying outliers in various situations in comparison to other existing approaches. This methodology extends to highdimensional modeling with p ≫ n, if both the coefficient vector and the outlier pattern are sparse.

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Section: Parameter Tuning In Outlier Detectionmentioning

confidence: 99%

Outlier Detection Using Nonconvex Penalized Regression

She

Owen

2011

Journal of the American Statistical Association

273

266

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“…The first such estimator was proposed by Stahel (1981a,b) and Donoho (1982) and it is recommended for small data sets, but the most widely used high breakdown estimator is the minimum covariance determinant estimate (Rousseeuw 1985). Several algorithms for computing the S estimators (Davies 1987) are provided (Ruppert 1992;Woodruff and Rocke 1994;Rocke 1996;Salibian-Barrera and Yohai 2006). The minimum volume ellipsoid (MVE) estimator (Rousseeuw 1985) is also included since it has some desirable properties when used as initial estimator for computing the S estimates (see Maronna et al 2006, p. 198).…”

Section: R> Library("rrcov")mentioning

confidence: 99%

An Object-Oriented Framework for Robust Multivariate Analysis

Todorov¹,

Filzmoser²

2009

J. Stat. Soft.

307

197

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Taking advantage of the S4 class system of the programming environment R, which facilitates the creation and maintenance of reusable and modular components, an objectoriented framework for robust multivariate analysis was developed. The framework resides in the packages robustbase and rrcov and includes an almost complete set of algorithms for computing robust multivariate location and scatter, various robust methods for principal component analysis as well as robust linear and quadratic discriminant analysis. The design of these methods follows common patterns which we call statistical design patterns in analogy to the design patterns widely used in software engineering. The application of the framework to data analysis as well as possible extensions by the development of new methods is demonstrated on examples which themselves are part of the package rrcov.

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“…It uses an S-estimator (Rousseeuw and Yohai, 1984) for the errors which is also computed with a bi-square score function. The S-estimator is computed using the Fast-S algorithm of Salibian-Barrera and Yohai (2006). Standard errors are computed using the formulas of Croux, Dhaene and Hoorelbeke (2003).…”

Section: Countrymentioning

confidence: 99%

Severance Pay Programs around the World: History, Rationale, Status, and Reforms

Holzmann

Pouget²,

Vodopivec

et al. 2011

Reforming Severance Pay

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. www.econstor.eu The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. Terms of use: Documents in D I S C U S S I O N P A P E R S E R I E SIZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author. The paper examines severance pay programs around the world by providing the first ever overview of existing programs, examining their historic development, assessing their economic rationale and describing current reform attempts. While a significant part of the paper is devoted to a comprehensive 183 cross country review of existing severance arrangements and their characteristics, the paper goes beyond a mere description. It develops and empirically tests three hypotheses about the economic rationale of the program, namely severance pay being: (i) a primitive income protection program, (ii) an efficiency enhancing human resource instrument, and (iii) a job protection instrument. The paper also reviews the recent reforms

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A Fast Algorithm for S-Regression Estimates

Cited by 186 publications

References 28 publications

Outlier Detection Using Nonconvex Penalized Regression

Outlier Detection Using Nonconvex Penalized Regression

An Object-Oriented Framework for Robust Multivariate Analysis

Severance Pay Programs around the World: History, Rationale, Status, and Reforms

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