Do Robust Estimators Work with Real Data?

Stigler, Stephen M.

doi:10.1214/aos/1176343997

Cited by 365 publications

(138 citation statements)

References 5 publications

Supporting

Mentioning

132

Contrasting

Order By: Relevance

“…Many robust estimation methods have been investigated and proposed since then, of which the most important classes include the sample median and the trimmed mean (see e.g. Stigler 1977;Welsh 1987), least absolute deviation or L 1 norm (see e.g. Bloomfield and Steiger 1983;Dodge 1997), robustified maximum likelihood or M-estimates (Huber 1964(Huber , 1981Andrews 1974;Hampel et al 1986;Jurecková and Sen 1996), order-based or L-estimates (Bickel 1973;Huber 1981;Hampel et al 1986;Jurecková and Sen 1996), and rank-based or R-estimates (Hodges and Lehmann 1963;Adichie 1967;Jurecková 1971;Jaeckel 1972;Koul 1977).…”

Section: Introductionmentioning

confidence: 99%

Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

2005

J Geodesy

123

View full text Add to dashboard Cite

The findings of this paper are summarized as follows: (1) We propose a sign-constrained robust estimation method, which can tolerate 50% of data contamination and meanwhile achieve high, least-squares-comparable efficiency. Since the objective function is identical with least squares, the method may also be called sign-constrained robust least squares. An iterative version of the method has been implemented and shown to be capable of resisting against more than 50% of contamination. As a by-product, a robust estimate of scale parameter can also be obtained. Unlike the least median of squares method and repeated medians, which use a least possible number of data to derive the solution, the signconstrained robust least squares method attempts to employ a maximum possible number of good data to derive the robust solution, and thus will not be affected by partial near multicollinearity among part of the data or if some of the data are clustered together; (2) although M-estimates have been reported to have a breakdown point of 1/(t + 1), we have shown that the weights of observations can readily deteriorate such results and bring the breakdown point of M-estimates of Huber's type to zero. The same zero breakdown point of the L 1 -norm method is also derived, again due to the weights of observations; (3) by assuming a prior distribution for the signs of outliers, we have developed the concept of subjective breakdown point, which may be thought of as an extension of stochastic breakdown by Donoho and Huber but can be important in explaining real-life problems in Earth Sciences and image reconstruction; and finally, (4) We have shown that the least median of squares method can still break down with a single outlier, even if no highly concentrated good data nor highly concentrated outliers exist.

show abstract

Section: Introductionmentioning

confidence: 99%

Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

2005

J Geodesy

123

View full text Add to dashboard Cite

show abstract

“…Wilcox (1997) also recommended 20%, and Mudholkar, Mudholkar and Srivastava (1991) suggested 15%. Ten percent has been considered by Hill and Dixon (1982), Huber (1977), Stigler (1977) and Staudte and Sheather (1990); results reported by Keselman, Wilcox, Othman and Fradette (2002) also support 10% trimming. Reed and Stark (1996) Keselman et al (in press), one can modify Reed and Stark's (1996) tail-length and skewness measures for the multi-group problem and then apply the modified multigroup measures to the hinge estimators.…”

Section: Adaptive Trimming Methodsmentioning

confidence: 72%

Robust Confidence Intervals for Effect Size in the Two-Group Case

Keselman

Algina

Fradette

2005

J. Mod. App. Stat. Meth.

View full text Add to dashboard Cite

The probability coverage of intervals involving robust estimates of effect size based on seven procedures was compared for asymmetrically trimming data in an independent two-groups design, and a method that symmetrically trims the data. Four conditions were varied: (a) percentage of trimming, (b) type of nonnormal population distribution, (c) population effect size, and (d) sample size. Results indicated that coverage probabilities were generally well controlled under the conditions of nonnormality. The symmetric trimming method provided excellent probability coverage. Recommendations are provided.

show abstract

“…, The entropy-difference statistics A33 m are implemented in our one-sample univariate data analysis computer program ONESAM. Table 3 lists autoregressive estimates of entropy-difference when testing for normality data sets in Stigler (1977). An asterisk indicates a data set which is not normal in our judgement.…”

Section: Resultsmentioning

confidence: 99%

Entropy Interpretation of Goodness of Fit Tests.

Parzen¹

1983

View full text Add to dashboard Cite

Do Robust Estimators Work with Real Data?

Cited by 365 publications

References 5 publications

Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

Robust Confidence Intervals for Effect Size in the Two-Group Case

Entropy Interpretation of Goodness of Fit Tests.

Contact Info

Product

Resources

About