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Using random subspace method for prediction and variable importance assessment in linear regression

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  • Mielniczuk, Jan
  • Teisseyre, Paweł

Abstract

A random subset method (RSM) with a new weighting scheme is proposed and investigated for linear regression with a large number of features. Weights of variables are defined as averages of squared values of pertaining t-statistics over fitted models with randomly chosen features. It is argued that such weighting is advisable as it incorporates two factors: a measure of importance of the variable within the considered model and a measure of goodness-of-fit of the model itself. Asymptotic weights assigned by such a scheme are determined as well as assumptions under which the method leads to consistent choice of significant variables in the model. Numerical experiments indicate that the proposed method behaves promisingly when its prediction errors are compared with errors of penalty-based methods such as the lasso and it has much smaller false discovery rate than the other methods considered.

Suggested Citation

  • Mielniczuk, Jan & Teisseyre, Paweł, 2014. "Using random subspace method for prediction and variable importance assessment in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 725-742.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:725-742
    DOI: 10.1016/j.csda.2012.09.018
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    References listed on IDEAS

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    Cited by:

    1. Łukasz Smaga & Hidetoshi Matsui, 2018. "A note on variable selection in functional regression via random subspace method," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 455-477, August.
    2. Thulin, Måns, 2014. "A high-dimensional two-sample test for the mean using random subspaces," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 26-38.
    3. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Paweł Teisseyre & Robert A. Kłopotek & Jan Mielniczuk, 2016. "Random Subspace Method for high-dimensional regression with the R package regRSM," Computational Statistics, Springer, vol. 31(3), pages 943-972, September.

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