Quadratic approximation on SCAD penalized estimation
In this paper, we propose a method of quadratic approximation that unifies various types of smoothly clipped absolute deviation (SCAD) penalized estimations. For convenience, we call it the quadratically approximated SCAD penalized estimation (Q-SCAD). We prove that the proposed Q-SCAD estimator achieves the oracle property and requires only the least angle regression (LARS) algorithm for computation. Numerical studies including simulations and real data analysis confirm that the Q-SCAD estimator performs as efficient as the original SCAD estimator.
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- Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
- Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
- Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
- Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
- Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
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