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Simultaneously identifying contributory variables and controlling the falsediscovery rate (FDR) in high-dimensional data is an important statisticalproblem. In this paper, we propose a novel model-free variable selectionprocedure in sufficient dimension reduction via data splitting technique. Thevariable selection problem is first connected with a least square procedurewith several response transformations. We construct a series of statistics withglobal symmetry property and then utilize the symmetry to derive a data-driventhreshold to achieve error rate control. This method can achieve finite-sampleand asymptotic FDR control under some mild conditions. Numerical experimentsindicate that our procedure has satisfactory FDR control and higher powercompared with existing methods.

Model-free controlled variable selection via data splitting