@article { ISI:000280072500005,
	title = {Uniform asymptotics for S- and MM-regression estimators},
	journal = {ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS},
	volume = {62},
	number = {5},
	year = {2010},
	month = {OCT},
	pages = {897-927},
	publisher = {SPRINGER HEIDELBERG},
	type = {Article},
	address = {TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY},
	abstract = {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{\textquoteright}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 Salibian-Barrera and Zamar for location-scale to the linear regression model.},
	keywords = {Robust inference, Robust regression, Robustness, Uniform asymptotics},
	issn = {0020-3157},
	doi = {10.1007/s10463-008-0189-x},
	author = {Omelka, Marek and Salibian-Barrera, Mat{\'\i}as}
}
@article { ISI:000254995100003,
	title = {Fast and robust bootstrap},
	journal = {STATISTICAL METHODS AND APPLICATIONS},
	volume = {17},
	number = {1},
	year = {2008},
	pages = {41-71},
	publisher = {SPRINGER HEIDELBERG},
	type = {Article},
	address = {TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY},
	abstract = {<p>In this paper we review recent developments on a bootstrap method for robust estimators which is computationally faster and more resistant to outliers than the classical bootstrap. This fast and robust bootstrap method is, under reasonable regularity conditions, asymptotically consistent. We describe the method in general and then consider its application to perform inference based on robust estimators for the linear regression and multivariate location-scatter models. In particular, we study confidence and prediction intervals and tests of hypotheses for linear regression models, inference for location-scatter parameters and principal components, and classification error estimation for discriminant analysis.</p>
},
	keywords = {bootstrap, PCA discriminant analysis, Robust inference, Robust regression},
	issn = {1618-2510},
	doi = {10.1007/s10260-007-0048-6},
	author = {Salibian-Barrera, Mat{\'\i}as and Van Aelst, Stefan and Willerns, Gert}
}
@article { ISI:000225197800015,
	title = {Estimating the p-values of robust tests for the linear model},
	journal = {JOURNAL OF STATISTICAL PLANNING AND INFERENCE},
	volume = {128},
	number = {1},
	year = {2005},
	month = {JAN 15},
	pages = {241-257},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {In this paper, we study the estimation of p-values for robust tests for the linear regression model. The asymptotic distribution of these tests has only been studied under the restrictive assumption of errors with known scale Or symmetric distribution. Since these robust tests are based on robust regression estimates, Efron{\textquoteright}s bootstrap (1979) presents a number of problems. In particular, it is computationally very expensive, and it is not resistant to outliers in the data. In other words, the tails of the bootstrap distribution estimates obtained by re-sampling the data may be severely affected by outliers. We show how to adapt the Robust Bootstrap (Ann. Statist 30 (2002) 556; Bootstrapping MM-estimators for linear regression with fixed designs, http://mathstat.carleton.ca/similar tomatias/pubs. html) to this problem. This method is very fast to compute, resistant to outliers in the data, and asymptotically correct under weak regularity assumptions. In this paper, we show that the Robust Bootstrap can be used to obtain asymptotically correct, computationally simple p-value estimates. A simulation study indicates that the tests whose p-values are estimated with the Robust Bootstrap have better finite sample significance levels than those obtained from the asymptotic theory based on the symmetry assumption. Although this paper is focussed on robust scores-type tests (in: Directions in Robust Statistics and Diagnostics, Part 1, Springer, New York), our approach can be applied to other robust tests (for example, Wald- and dispersion-type also discussed in Markatou et a]., 1991). (C) 2003 Elsevier B.V. All rights reserved.},
	keywords = {bootstrap, Robust inference, Robust regression, scores test, Wald test},
	issn = {0378-3758},
	doi = {10.1016/j.jspi.2003.09.033},
	author = {Salibian-Barrera, M}
}
@article { ISI:000223519100004,
	title = {Uniform asymptotics for robust location estimates when the scale is unknown},
	journal = {ANNALS OF STATISTICS},
	volume = {32},
	number = {4},
	year = {2004},
	month = {AUG},
	pages = {1434-1447},
	publisher = {INST MATHEMATICAL STATISTICS},
	type = {Article},
	address = {PO BOX 22718, BEACHWOOD, OH 44122 USA},
	abstract = {Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verily in practice. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data remains largely unspecified and hence results that hold uniformly over a set of possible distribution functions are of theoretical and practical interest. Also, it is desirable to be able to determine the size of the set of distribution functions where the uniform properties hold. In this paper we study the problem of obtaining verifiable regularity conditions that suffice to yield uniform consistency and uniform asymptotic normality for location robust estimates when the scale of the errors is unknown. We study M-location estimates calculated with an S-scale and we obtain uniform asymptotic results over contamination neighborhoods. Moreover, we show how to calculate the maximum size of the contamination neighborhoods where these uniform results hold. There is a trade-off between the size of these neighborhoods and the breakdown point of the scale estimate.},
	keywords = {M-estimates, Robust inference, robust location and scale models, Robustness},
	issn = {0090-5364},
	doi = {10.1214/009053604000000544},
	author = {Salibian-Barrera, M and Zamar, RH}
}
