Omelka, Marek; Salibián-Barrera, Matías Uniform asymptotics for S- and MM-regression estimators. (English) Zbl 1432.62210 Ann. Inst. Stat. Math. 62, No. 5, 897-927 (2010). Summary: In this paper we find verifiable regularity conditions to ensure that S-estimators of scale and regression and MM-estimators of regression are uniformly consistent and uniformly asymptotically normally distributed over contamination neighbourhoods. Moreover, we show how to calculate the size of these neighbourhoods. In particular, we find that, for MM-estimators computed with Tukey’s family of bisquare score functions, there is a trade-off between the size of these neighbourhoods and both the breakdown point of the S-estimators and the leverage of the contamination that is allowed in the neighbourhood. These results extend previous work of the second author and R. H. Zamar [Ann. Stat. 32, No. 4, 1434–1447 (2004; Zbl 1047.62022)] for location-scale to the linear regression model. Cited in 2 Documents MSC: 62J05 Linear regression; mixed models 62F12 Asymptotic properties of parametric estimators 62F35 Robustness and adaptive procedures (parametric inference) Keywords:robustness; robust inference; uniform asymptotics; robust regression Citations:Zbl 1047.62022 PDFBibTeX XMLCite \textit{M. Omelka} and \textit{M. Salibián-Barrera}, Ann. Inst. Stat. Math. 62, No. 5, 897--927 (2010; Zbl 1432.62210) Full Text: DOI References: [1] Beaton A.E., Tukey J.W. (1974) The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics 16: 147–185 · Zbl 0282.62057 [2] Berrendero J.R., Zamar R.H. (1999) Global robustness of location and dispersion estimates. Statistics and Probability Letters 44: 63–72 · Zbl 0940.62029 [3] Berrendero J.R., Zamar R.H. (2006) A note on the uniform asymptotic normality of location M-estimates. Metrika 63: 55–69 · Zbl 1095.62027 [4] Bickel P.J. (1975) One-step Huber estimates in the linear model. 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