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Predictor ranking and false discovery proportion control in high-dimensional regression

Author

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  • Jeng, X. Jessie
  • Chen, Xiongzhi

Abstract

We propose a ranking and selection procedure to prioritize relevant predictors and control false discovery proportion (FDP) in variable selection. Our procedure utilizes a new ranking method built upon the de-sparsified Lasso estimator. We show that the new ranking method achieves the optimal order of minimum non-zero effects in ranking relevant predictors ahead of irrelevant ones. Adopting the new ranking method, we develop a variable selection procedure to asymptotically control FDP at a user-specified level. We show that our procedure can consistently estimate the FDP of variable selection as long as the de-sparsified Lasso estimator is asymptotically normal. In simulations, our procedure compares favorably to existing methods in ranking efficiency and FDP control when the regression model is relatively sparse.

Suggested Citation

  • Jeng, X. Jessie & Chen, Xiongzhi, 2019. "Predictor ranking and false discovery proportion control in high-dimensional regression," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 163-175.
  • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:163-175
    DOI: 10.1016/j.jmva.2018.12.006
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    References listed on IDEAS

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    1. 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.
    2. Max Grazier G'Sell & Stefan Wager & Alexandra Chouldechova & Robert Tibshirani, 2016. "Sequential selection procedures and false discovery rate control," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 423-444, March.
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    4. Sun, Wenguang & Cai, T. Tony, 2007. "Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 901-912, September.
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    8. Christopher Genovese & Larry Wasserman, 2002. "Operating characteristics and extensions of the false discovery rate procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 499-517, August.
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