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Variable selection via combined penalization for high-dimensional data analysis

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  • Wang, Xiaoming
  • Park, Taesung
  • Carriere, K.C.

Abstract

We propose a new penalized least squares approach to handling high-dimensional statistical analysis problems. Our proposed procedure can outperform the SCAD penalty technique (Fan and Li, 2001) when the number of predictors p is much larger than the number of observations n, and/or when the correlation among predictors is high. The proposed procedure has some of the properties of the smoothly clipped absolute deviation (SCAD) penalty method, including sparsity and continuity, and is asymptotically equivalent to an oracle estimator. We show how the approach can be used to analyze high-dimensional data, e.g., microarray data, to construct a classification rule and at the same time automatically select significant genes. A simulation study and real data examples demonstrate the practical aspects of the new method.

Suggested Citation

  • Wang, Xiaoming & Park, Taesung & Carriere, K.C., 2010. "Variable selection via combined penalization for high-dimensional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2230-2243, October.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:10:p:2230-2243
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    References listed on IDEAS

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    1. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    2. 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.
    3. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    4. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    2. Wenya Liu & Qi Li, 2017. "An Efficient Elastic Net with Regression Coefficients Method for Variable Selection of Spectrum Data," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-13, February.
    3. Roberts, S. & Nowak, G., 2014. "Stabilizing the lasso against cross-validation variability," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 198-211.
    4. Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.

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