@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.} }