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Variable selection after screening: with or without data splitting?

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  • Xiaoyi Zhu
  • Yuhong Yang

Abstract

High dimensional data sets are now frequently encountered in many scientific fields. In order to select a sparse set of predictors that have predictive power and/or provide insightful understanding on which predictors really influence the response, a preliminary variable screening is typically done often informally. Fan and Lv (J R Stat Soc Ser B 70:849–911, 2008 ) proposed sure independence screening (SIS) to reduce the dimension of the set of predictors from ultra-high to a moderate scale below the sample size. Then one may apply a familiar variable selection technique. While this approach has become popular, the screening bias issue has been mainly ignored. The screening bias may lead to the final selection of a number of predictors that have no/little value for prediction/explanation. In this paper we set to examine this screening bias both theoretically and numerically compare the approach with an alternative that utilizes data splitting. The simulation results and real bioinformatics examples show that data splitting can significantly reduce the screening bias for variable selection and improve the prediction accuracy as well. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Xiaoyi Zhu & Yuhong Yang, 2015. "Variable selection after screening: with or without data splitting?," Computational Statistics, Springer, vol. 30(1), pages 191-203, March.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:1:p:191-203
    DOI: 10.1007/s00180-014-0528-8
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    References listed on IDEAS

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    1. 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.
    2. Meinshausen, Nicolai & Meier, Lukas & Bühlmann, Peter, 2009. "p-Values for High-Dimensional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1671-1681.
    3. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    4. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    5. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
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    1. Chun-Xia Zhang & Jiang-She Zhang & Sang-Woon Kim, 2016. "PBoostGA: pseudo-boosting genetic algorithm for variable ranking and selection," Computational Statistics, Springer, vol. 31(4), pages 1237-1262, December.

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