@article { ISI:000319173400020,
	title = {Robust and efficient estimation of the residual scale in linear regression},
	journal = {JOURNAL OF MULTIVARIATE ANALYSIS},
	volume = {116},
	year = {2013},
	month = {APR},
	pages = {278-296},
	publisher = {ELSEVIER INC},
	type = {Article},
	address = {525 B STREET, STE 1900, SAN DIEGO, CA 92101-4495 USA},
	abstract = {Robustness and efficiency of the residual scale estimators in the regression model is important for robust inference. We introduce the class of robust generalized M-scale estimators for the regression model, derive their influence function and gross-error sensitivity, and study their maxbias behavior. In particular, we find overall minimax bias estimates for the general class and also for well-known subclasses. We pose and solve a Hampers-like optimality problem: we find generalized M-scale estimators with maximal efficiency subject to a lower bound on the global and local robustness of the estimators. (C) 2013 Elsevier Inc. All rights reserved.},
	keywords = {Efficiency, Gross-error sensitivity, influence function, Maxbias, Robust scale},
	issn = {0047-259X},
	doi = {10.1016/j.jmva.2012.12.008},
	author = {Van Aelst, Stefan and Willems, Gert and Zamar, Ruben H.}
}
@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}
}
