@article { ISI:000258196500027,
	title = {Robust estimation of error scale in nonparametric regression models},
	journal = {JOURNAL OF STATISTICAL PLANNING AND INFERENCE},
	volume = {138},
	number = {10},
	year = {2008},
	month = {OCT 1},
	pages = {3200-3216},
	publisher = {ELSEVIER SCIENCE BV},
	type = {Article},
	address = {PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS},
	abstract = {When the data used to fit a nonparametric regression model are contaminated with outliers, we need to use a robust estimator of scale in order to make robust estimation of the regression function possible. We develop a family of M-estimators of scale constructed from consecutive differences of regression responses. Estimators in our family robustify the estimator proposed by Rice [1984. Bandwidth choice for nonparametric regression. Ann. Statist. 12, 1215-1230]. Under appropriate conditions, we establish the weak consistency and asymptotic normality of all estimators in our family. Estimators in our family vary in terms of their robustness properties. We quantify the robustness of each estimator via the maxbias. We use this measure as a basis for deriving the asymptotic breakdown point of the estimator. Our theoretical results allow us to specify conditions for estimators in our family to achieve a maximum asymptotic breakdown point of 1/2. We conduct a simulation study to compare the finite sample performance of our preferred M-estimator with that of three other estimators. (C) 2008 Elsevier B.V. All rights reserved.},
	keywords = {asymptotic breakdown point, consecutive differences, error scale, fixed design, M-scale estimator, M-scale functional, Maxbias, nonparametric regression, Outliers, robust},
	issn = {0378-3758},
	doi = {10.1016/j.jspi.2008.01.005},
	author = {Ghement, Isabella Rodica and Ruiz, Marcelo and Zamar, Ruben}
}
@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}
}
