An approach to estimating nonlinear sufficient dimension reduction subspace for censored survival data

An approach was proposed to estimating the nonlinear sufficient dimension reduction (SDR) subspace for survival data with censorship. Based on the theory of reproducing kernel Hilbert spaces (RKHS) and the double slicing procedure，the joint nonlinear sufficient dimension reduction central subspace was estimated by means of the generalized eigen-decomposition equation. And the weight function was estimated by the definition and property of SDR central subspace. The efficiency was improved by the iteration method while the algorithm was being implemented. Finally， the performance of the proposed method was illustrated on simulated data.