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Quadratic approximation on SCAD penalized estimation

  • Kwon, Sunghoon
  • Choi, Hosik
  • Kim, Yongdai
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    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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    File URL: http://www.sciencedirect.com/science/article/B6V8V-506RMPS-1/2/77e02914e01063be3589aa194b47cb82
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 1 (January)
    Pages: 421-428

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:421-428
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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