Journal article
Efficient robust regression via two-stage generalized empirical likelihood
HD Bondell, LA Stefanski
Journal of the American Statistical Association | AMER STATISTICAL ASSOC | Published : 2013
Abstract
Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency is obtained from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample replacement breakdown point and full asymptotic efficiency for normal errors. Simulation evidence shows that compared to existing robust regression estimators, the new estimator has relatively high efficiency for small sa..
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Awarded by National Science Foundation
Funding Acknowledgements
Howard D. Bondell is Associate Professor, Department of Statistics, North Carolina State University, Raleigh, NC 27695 (E-mail: bondell@stat.ncsu.edu). Leonard A. Stefanski is Professor, Department of Statistics, North Carolina State University, Raleigh, NC 27695 (E-mail: stefansk@ncsu.edu). The authors are grateful to the editor, an associate editor, and three anonymous referees for their valuable comments. The authors' research was partially supported by NSF grant DMS 1005612 and NIH grants P01-CA-142538, R01-MH-084022 (Bondell); and NSF grant DMS 0906421 and NIH grants R01-CA-085848, P01-CA-142538 (Stefanski).