Consistent significance controlled variable selection in high‐dimensional regression

Abstract

In regression analysis, selecting, out of a pool of available predictors, those that compose the true underlying data‐generating mechanism is a fundamental part of model building. This paper introduces a forward selection method that uses a novel entry criterium based on a combination of p‐values of the predictors already selected. Moreover, the proposed variable selection procedure controls the significance of all selected predictors at each step using False Discovery Rate corrections (or Bonferroni, or other correction criteria). Monte Carlo simulations suggest that the proposed method performs competitively against classical competitors. The proposed variable selection procedure is illustrated on a real data set.