Robust Statistics

Maronna, Ricardo A.; Martin, R. Douglas; Yohai, Vı́ctor J.

doi:10.1002/0470010940

Cited by 1,787 publications

(1,076 citation statements)

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“…Although the Type I error rate is widely viewed as being relatively unaffected by non-normality, Bradley (1980) has pointed out conditions in which this is not true. This finding is also evident in the findings of recent studies and published texts (e. g., See Hempel, Ronchetti, & Rousseeuw, 1986;Huber & Ronchetti, 2009;Maronna, Martin, & Yohai, 2006;Micceri, 1989;Schoder, et al, 2006;Staudte & Sheather, 1990;Wilcox, 2012a, b;Wilcox & Keselman, 2003).…”

Section: Introductionsupporting

confidence: 64%

Preliminary Testing for Normality: Is This a Good Practice?

Keselman

Othman

Wilcox

2013

J. Mod. App. Stat. Meth.

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Section: Introductionsupporting

confidence: 64%

Preliminary Testing for Normality: Is This a Good Practice?

Keselman

Othman

Wilcox

2013

J. Mod. App. Stat. Meth.

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“…It is worth mentioning that outlier identification and robust regression are two closely related but not quite identical problems (Rousseeuw & Leroy 1987;Maronna et al 2006). Even if we perfectly identified the regression coefficient vector, there could still be some overlap between the residual distributions for good and outlying points.…”

Section: Survey Of Robust Regressionmentioning

confidence: 88%

Outlier Detection Using Nonconvex Penalized Regression

She

Owen

2011

Journal of the American Statistical Association

268

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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“…The standard choice for the tuning constant b is 3.5; however, any value for b within 3 and 4 seems appropriate (see Maronna et al (2006) for a discussion of the choice for b in a general context). On one hand, outliers might receive too much weight when b is larger than 4.…”

Section: The Rebs Techniquementioning

confidence: 99%

Robust extraction of baseline signal of atmospheric trace species using local regression

et al. 2012

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Abstract. The identification of atmospheric trace species measurements that are representative of well-mixed background air masses is required for monitoring atmospheric composition change at background sites. We present a statistical method based on robust local regression that is well suited for the selection of background measurements and the estimation of associated baseline curves. The bootstrap technique is applied to calculate the uncertainty in the resulting baseline curve. The non-parametric nature of the proposed approach makes it a very flexible data filtering method. The determined average annual change of CO at Jungfraujoch for the 1996 to 2009 period as estimated from filtered annual mean CO concentrations is −2.2 ± 1.1 ppb yr −1 . For comparison, the linear trend of unfiltered CO measurements at Jungfraujoch for this time period is −2.9 ± 1.3 ppb yr −1 .

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Robust Statistics

Cited by 1,787 publications

References 0 publications

Preliminary Testing for Normality: Is This a Good Practice?

Preliminary Testing for Normality: Is This a Good Practice?

Outlier Detection Using Nonconvex Penalized Regression

Robust extraction of baseline signal of atmospheric trace species using local regression

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