摘要：We present a new methodology for nonlinear dimension reduction for survival data by using the theory of reproducing kernel Hilbert space (RKHS). By means of the double slicing procedure and the kernel-based method of transforming the infinite dimension case into finite dimension one, we build kernel sliced inverse regression in a RKHS rigorously. The resulting estimator of the nonlinear efficient dimension reduction variates is shown to be consistent under some regularity conditions. Simulations are used to illustrate the efficacy of the method. 

Key words: Reproducing kernel Hilbert space, censored data, nonlinear dimension reduction, double slicing procedure.