Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection
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A data‐driven weighted linear combination of convex loss functions, together with weighted L1‐penalty is proposed and established a strong oracle property of the method proposed that has both the model selection consistency and estimation efficiency for the true non‐zero coefficients.Abstract:
In high-dimensional model selection problems, penalized least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a data-driven weighted linear combination of convex loss functions, together with weighted L1-penalty. It is completely data-adaptive and does not require prior knowledge of the error distribution. The weighted L1-penalty is used both to ensure the convexity of the penalty term and to ameliorate the bias caused by the L1-penalty. In the setting with dimensionality much larger than the sample size, we establish a strong oracle property of the proposed method that possesses both the model selection consistency and estimation efficiency for the true non-zero coefficients. As specific examples, we introduce a robust method of composite L1-L2, and optimal composite quantile method and evaluate their performance in both simulated and real data examples.read more
Citations
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References
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Ming Yuan,Yi Lin +1 more
TL;DR: In this article, the non-negative garrotte estimator can be used in combination with estimators other than the original least squares estimator as in its original form, such as the lasso, the elastic net and ridge regression along with ordinary least squares as the initial estimate.
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L1-Norm Quantile Regression
Youjuan Li,Ji Zhu +1 more
TL;DR: In this article, the LASSO regularized quantile regression (L1-norm QR) model is proposed, which uses the sum of the absolute values of the coefficients as the penalty.
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