Regression with outlier shrinkage |
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Authors: | Shifeng Xiong V. Roshan Joseph |
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Affiliation: | 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, United States |
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Abstract: | We propose a robust regression method called regression with outlier shrinkage (ROS) for the traditional n>p cases. It improves over the other robust regression methods such as least trimmed squares (LTS) in the sense that it can achieve maximum breakdown value and full asymptotic efficiency simultaneously. Moreover, its computational complexity is no more than that of LTS. We also propose a sparse estimator, called sparse regression with outlier shrinkage (SROS), for robust variable selection and estimation. It is proven that SROS can not only give consistent selection but also estimate the nonzero coefficients with full asymptotic efficiency under the normal model. In addition, we introduce a concept of nearly regression equivariant estimator for understanding the breakdown properties of sparse estimators, and prove that SROS achieves the maximum breakdown value of nearly regression equivariant estimators. Numerical examples are presented to illustrate our methods. |
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Keywords: | Breakdown value Penalized regression Robust regression Variable selection Weighted least squares |
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