Robust and efficient estimation of the residual scale in linear regression

Stefan Van Aelst, Gert Willems and Ruben H. Zamar

Journal of Multivariate Analysis, 2013, vol. 116, issue C, 278-296

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.

Keywords: Robust scale; Maxbias; Influence function; Gross-error sensitivity; Efficiency (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2012.12.008

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