New Robust Variable Selection Methods for Linear Regression Models |
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Authors: | Ziqi Chen Man‐Lai Tang Wei Gao Ning‐Zhong Shi |
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Institution: | 1. School of Mathematics and Statistics, Central South University;2. Department of Mathematics and Statistics, Hang Seng Management College;3. Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University |
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Abstract: | Motivated by an entropy inequality, we propose for the first time a penalized profile likelihood method for simultaneously selecting significant variables and estimating unknown coefficients in multiple linear regression models in this article. The new method is robust to outliers or errors with heavy tails and works well even for error with infinite variance. Our proposed approach outperforms the adaptive lasso in both theory and practice. It is observed from the simulation studies that (i) the new approach possesses higher probability of correctly selecting the exact model than the least absolute deviation lasso and the adaptively penalized composite quantile regression approach and (ii) exact model selection via our proposed approach is robust regardless of the error distribution. An application to a real dataset is also provided. |
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Keywords: | adaptive lasso entropy inequality oracle properties penalized profile likelihood profile likelihood robustness variable selection |
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