@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:000265170600008,
	title = {Bayesian likelihood robustness in linear models},
	journal = {JOURNAL OF STATISTICAL PLANNING AND INFERENCE},
	volume = {139},
	number = {7},
	year = {2009},
	month = {JUL 1},
	pages = {2196-2207},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {This paper deals with the problem of robustness of Bayesian regression with respect to the data. We first give a formal definition of Bayesian robustness to data contamination, prove that robustness according to the definition cannot be obtained by using heavy-tailed error distributions in linear regression models and propose a heteroscedastic approach to achieve the desired Bayesian robustness. (C) 2008 Elsevier B.V. All rights reserved.},
	keywords = {Bayesian inference, Heteroscedasticity, Kullback-Leibler divergence, Robust regression},
	issn = {0378-3758},
	doi = {10.1016/j.jspi.2008.10.012},
	author = {Pena, Daniel and Zamar, Ruben and Yan, Guohua}
}
@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:000259127900007,
	title = {The fast-tau estimator for regression},
	journal = {JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS},
	volume = {17},
	number = {3},
	year = {2008},
	month = {SEP},
	pages = {659-682},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {732 N WASHINGTON ST, ALEXANDRIA, VA 22314-1943 USA},
	abstract = {<p>Yohai and Zamar{\textquoteright}s tau-estimators of regression have excellent statistical properties but are nevertheless rarely used in practice because of a lack of available software and the general impression that tau-estimators are difficult to approximate. We will show, however, that the computational difficulties of approximating tau-estimators are similar in nature to those of the more popular S-estimators. The main goal of this article is to compare an approximating algorithm for tau-estimators based on random resampling with some alternative heuristic search algorithms. We show that the former is not only simpler, but that when enhanced by local improvement steps it generally outperforms the considered heuristic search algorithms, even when these heuristic algorithms also incorporate local improvement steps. Additionally, we show that the random resampling algorithm for approximating tau-estimators has favorable statistical properties compared to the analogous and widely used algorithms for S- and least trimmed squares estimators.</p>
},
	keywords = {random resampling, Robust regression, simulated annealing, tabu search},
	issn = {1061-8600},
	doi = {10.1198/106186008X343785},
	author = {Salibian-Barrera, Mat{\'\i}as and Willems, Gert and Zamar, Ruben}
}
@article { ISI:000259127900007,
	title = {The fast-tau estimator for regression},
	journal = {JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS},
	volume = {17},
	number = {3},
	year = {2008},
	month = {SEP},
	pages = {659-682},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {732 N WASHINGTON ST, ALEXANDRIA, VA 22314-1943 USA},
	abstract = {Yohai and Zamar{\textquoteright}s tau-estimators of regression have excellent statistical properties but are nevertheless rarely used in practice because of a lack of available software and the general impression that tau-estimators are difficult to approximate. We will show, however, that the computational difficulties of approximating tau-estimators are similar in nature to those of the more popular S-estimators. The main goal of this article is to compare an approximating algorithm for tau-estimators based on random resampling with some alternative heuristic search algorithms. We show that the former is not only simpler, but that when enhanced by local improvement steps it generally outperforms the considered heuristic search algorithms, even when these heuristic algorithms also incorporate local improvement steps. Additionally, we show that the random resampling algorithm for approximating tau-estimators has favorable statistical properties compared to the analogous and widely used algorithms for S- and least trimmed squares estimators.},
	keywords = {random resampling, Robust regression, simulated annealing, tabu search},
	issn = {1061-8600},
	doi = {10.1198/106186008X343785},
	author = {Salibian-Barrera, Mat{\'\i}as and Willems, Gert and Zamar, Ruben}
}
@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}
}
