Model-free variable selection in sufficient dimension reduction via FDR control

Simultaneously identifying contributory variables and controlling the false discovery rate (FDR) in high-dimensional data is an important statistical problem. In this paper, we propose a novel model-free variable selection procedure in sufficient dimension reduction via data splitting technique. The variable selection problem is first connected with a least square procedure with several response transformations. We construct a series of statistics with global symmetry property and then utilize the symmetry to derive a data-driven threshold to achieve error rate control. This method can achieve finite-sample and asymptotic FDR control under some mild conditions. Numerical experiments indicate that our procedure has satisfactory FDR control and higher power compared with existing methods.