Robust and efficient estimation of the residual scale in linear regression

Authors:
Stefan Van Aelst;Gert Willems;Ruben H. Zamar
Affiliations:
Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium;Department of Statistics, University of British Columbia, 6356 Agricultural Road, Vancouver, BC, Canada V6T-1Z2
Venue:
Journal of Multivariate Analysis
Year:
2013

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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 Hampel's-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.