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Quadratic approximation for nonconvex penalized estimations with a diverging number of parameters

  • Lee, Sangin
  • Kim, Yongdai
  • Kwon, Sunghoon
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    We propose an approximated penalized estimator (APE) that covers various statistical models and nonconvex penalties including the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) as a special case. The APE achieves the oracle property with a diverging number of parameters which extends the results of Kwon et al. (2011). Several numerical studies confirm the theoretical results.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 9 ()
    Pages: 1710-1717

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1710-1717
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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 & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683.
    3. 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.
    4. He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
    5. Yongdai Kim & Sunghoon Kwon, 2012. "Global optimality of nonconvex penalized estimators," Biometrika, Biometrika Trust, vol. 99(2), pages 315-325.
    6. Kwon, Sunghoon & Choi, Hosik & Kim, Yongdai, 2011. "Quadratic approximation on SCAD penalized estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 421-428, January.
    7. Leng, Chenlei & Li, Bo, 2010. "Least squares approximation with a diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 254-261, February.
    8. 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.
    9. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    10. Clifford Lam & Jianqing Fan, 2008. "Profile-kernel likelihood inference with diverging number of parameters," LSE Research Online Documents on Economics 31548, London School of Economics and Political Science, LSE Library.
    11. 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.
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