Quadratic approximation for nonconvex penalized estimations with a diverging number of parameters
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.
Volume (Year): 82 (2012)
Issue (Month): 9 ()
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- 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.
- 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.
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- 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.
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- 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.
- Yongdai Kim & Sunghoon Kwon, 2012. "Global optimality of nonconvex penalized estimators," Biometrika, Biometrika Trust, vol. 99(2), pages 315-325.
- 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.
- 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.
- 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.
- 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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