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High-dimensional variable screening and bias in subsequent inference, with an empirical comparison

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  • Peter Bühlmann
  • Jacopo Mandozzi

Abstract

We review variable selection and variable screening in high-dimensional linear models. Thereby, a major focus is an empirical comparison of various estimation methods with respect to true and false positive selection rates based on 128 different sparse scenarios from semi-real data (real data covariables but synthetic regression coefficients and noise). Furthermore, we present some theoretical bounds for the bias in subsequent least squares estimation, using the selected variables from the first stage, which have direct implications for construction of p-values for regression coefficients. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • 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.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:407-430
    DOI: 10.1007/s00180-013-0436-3
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    References listed on IDEAS

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    Cited by:

    1. Nickolay Trendafilov & Martin Kleinsteuber & Hui Zou, 2014. "Sparse matrices in data analysis," Computational Statistics, Springer, vol. 29(3), pages 403-405, June.
    2. Shi, Chengchun & Song, Rui & Lu, Wenbin & Li, Runzi, 2020. "Statistical inference for high-dimensional models via recursive online-score estimation," LSE Research Online Documents on Economics 103043, London School of Economics and Political Science, LSE Library.
    3. Luke Mosley & Idris A. Eckley & Alex Gibberd, 2022. "Sparse temporal disaggregation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2203-2233, October.
    4. Xiaoyi Zhu & Yuhong Yang, 2015. "Variable selection after screening: with or without data splitting?," Computational Statistics, Springer, vol. 30(1), pages 191-203, March.
    5. Guillermo Durand & Gilles Blanchard & Pierre Neuvial & Etienne Roquain, 2020. "Post hoc false positive control for structured hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1114-1148, December.
    6. 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.
    7. Claude Renaux & Laura Buzdugan & Markus Kalisch & Peter Bühlmann, 2020. "Hierarchical inference for genome-wide association studies: a view on methodology with software," Computational Statistics, Springer, vol. 35(1), pages 1-40, March.
    8. Luke Mosley & Idris Eckley & Alex Gibberd, 2021. "Sparse Temporal Disaggregation," Papers 2108.05783, arXiv.org, revised Oct 2022.

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