A new reproducing kernel‐based nonlinear dimension reduction method for survival data

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism constructed based RKHS property, then function in can be represented by inner product two elements that reside isomorphic feature space. Due censorship data, double slicing used estimate weight adjust censoring bias. The sufficient (SDR) subspace estimated generalized eigen-decomposition problem. asymptotic property estimator established perturbation theory. Finally, performance illustrated simulated real data. numerical results show comparable with linear SDR method. Most importantly, also effectively extract nonlinearity from