Threshold Selection in Feature Screening for Error Rate Control

Hard thresholding rule is commonly adopted in feature screening procedures to screen out unimportant predictors for ultrahigh-dimensional data. However, different thresholds are required adapt contexts of problems and an appropriate magnitude usually varies from the model error distribution. With ad-hoc choice, it unclear whether all important selected or not, very likely that would include many features. We introduce a data-adaptive threshold selection procedure with rate control, which applicable most kinds popular methods. The key idea apply sample-splitting strategy construct series statistics marginal symmetry property then utilize obtaining approximation number false discoveries. show proposed method able asymptotically control discovery per family under certain conditions still retains predictors. Three examples presented illustrate merits new procedures. Numerical experiments indicate methodology works well existing Supplementary materials this article available online.