Stability under contamination of robust regression estimators based on differences of residuals |
| |
| Institution: | 1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, China;2. Department of Mathematics and Statistics, Yunnan University, Kunming, 650031, China;1. School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham B15 2TT, UK;2. Integrated Research on Energy, Environment and Society, Energy and Sustainability Research Institute Groningen, University of Groningen, Groningen 9747 AG, Netherlands;3. College of Economics and Management & Research Centre for Soft Energy Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;4. The Bartlett School of Sustainable Construction, University College London, London WC1E 6BT, UK;5. Industrial Ecology Programme, Norwegian University of Science and Technology, Trondheim 7491, Norway;6. Department of Earth System Science, Tsinghua University, Beijing 100871, China;7. Institute of Blue and Green Development, Shandong University, Weihai 264209, China;8. Key Laboratory of City Cluster Environmental Safety and Green Development, Ministry of Education, School of Ecology, Environment and Resources, Guangdong University of Technology, Guangzhou 510006, China;9. School of Economics and Management, China University of Geosciences, Beijing 100083, China;1. Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, United States;2. Equipe Géostatistique, Centre de Géosciences, Mines ParisTech, Fontainebleau, France |
| |
| Abstract: | A reasonable approach to robust regression estimation is minimizing a robust scale estimator of the pairwise differences of residuals. We introduce a large class of estimators based on this strategy extending ideas of Yohai and Zamar (Am. Statist. (1993) 1824–1842) and Croux et al. (J. Am. Statist. Assoc. (1994) 1271–1281). The asymptotic robustness properties of the estimators in this class are addressed using the maxbias curve. We provide a general principle to compute this curve and present explicit formulae for several particular cases including generalized versions of S-, R- and τ-estimators. Finally, the most stable estimator in the class, that is, the estimator with the minimum maxbias curve, is shown to be the set of coefficients that minimizes an appropriate quantile of the distribution of the absolute pairwise differences of residuals. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
