Robust and efficient estimation of the residual scale in linear regression

JOURNAL OF MULTIVARIATE ANALYSIS

卷:116

Article

Van Aelst, Stefan¹  Willems, Gert¹  Zamar, Ruben H.² 

[1] Univ Ghent, Dept Appl Math & Comp Sci, B-9000 Ghent, Belgium

[2] Univ British Columbia, Dept Stat, Vancouver, BC V6T 1Z2, Canada

关键词: Robust scale;    Maxbias;    Influence function;    Gross-error sensitivity;    Efficiency;   

DOI  :  10.1016/j.jmva.2012.12.008

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free