@article { ISI:000237190100003,
	title = {The asymptotics of MM-estimators for linear regression with fixed designs},
	journal = {METRIKA},
	volume = {63},
	number = {3},
	year = {2006},
	month = {JUN},
	pages = {283-294},
	publisher = {PHYSICA-VERLAG GMBH \& CO},
	type = {Article},
	address = {PO BOX 10 52 80, 69042 HEIDELBERG, GERMANY},
	abstract = {MM-estimators achieve simultaneous high efficiency and high breakdown point over contamination neighborhoods. Inference based on these estimators relies on their asymptotic properties, which have been studied for the case of random covariates. In this paper we show that, under relatively mild regularity conditions, MM-estimators for linear regression models are strongly consistent when the design is fixed. Moreover, their strong consistency allows us to show that these estimators are also asymptotically normal for non-random covariates. These results justify the use of a normal approximation to the finite-sample distribution of MM-estimators for linear regression with fixed explanatory variables. Additionally, these results have been used to extend the robust bootstrap (Salibian-Barrera and Zamar in Ann Stat 30:556-582, 2002) to the case of fixed designs [see Salibian-Barrera 2004, submitted].},
	keywords = {asymptotic distribution, consistency, fixed designs, MM-estimators},
	issn = {0026-1335},
	doi = {10.1007/s00184-005-0019-6},
	author = {Salibian-Barrera, M}
}
@article { ISI:000238028100013,
	title = {Bootstrapping MM-estimators for linear regression with fixed designs},
	journal = {STATISTICS \& PROBABILITY LETTERS},
	volume = {76},
	number = {12},
	year = {2006},
	month = {JUL 1},
	pages = {1287-1297},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {In this paper, I study the extension of the robust bootstrap [Salibian-Barrera, M., Zarnar, R.H., 2002. Bootstrapping robust estimates of regression. Ann. Statist. 30, 556-582] to the case of fixed designs. The robust bootstrap is a computer-intensive inference method for robust regression estimators which is computationally simple (because we do not need to recompute the robust estimate with each bootstrap sample) and robust to the presence of outliers in the bootstrap samples. In this paper, I prove the consistency of this method for the case of non-random explanatory variables and illustrate its use on a real data set. Simulation results indicate that confidence intervals based on the robust bootstrap have good finite-sample coverage levels. (C) 2006 Elsevier B.V. All rights reserved.},
	keywords = {bootstrap, fixed design, inference, linear regression, MM-estimators, Robustness},
	issn = {0167-7152},
	doi = {10.1016/j.spl.2006.01.008},
	author = {Salibian-Barrera, M}
}
@article { ISI:000240158700035,
	title = {Principal components analysis based on multivariate MM estimators with fast and robust bootstrap},
	journal = {JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION},
	volume = {101},
	number = {475},
	year = {2006},
	month = {SEP},
	pages = {1198-1211},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {1429 DUKE ST, ALEXANDRIA, VA 22314 USA},
	abstract = {We consider robust principal components analysis (PCA) based on multivariate MM estimators. We first study the robustness and efficiency of these estimators, particularly in terms of eigenvalues and eigenvectors. We then focus on inference procedures based on a fast and robust bootstrap for MM estimators. This method is an alternative to the approach based on the asymptotic distribution of the estimators and can also be used to assess the stability of the principal components. A formal consistency proof for the bootstrap method is given, and its finite-sample performance is investigated through simulations. We illustrate the use of the robust PCA and the bootstrap inference on a real dataset.},
	keywords = {bootstrap, inference, MM-estimators, Principal components, Robustness},
	issn = {0162-1459},
	doi = {10.1198/016214506000000096},
	author = {Salibian-Barrera, Mat{\'\i}as and Van Aelst, Stefan and Willems, Gert}
}
