Sparse SIR:Optimal Rates And Adaptive Estimation

Sliced inverse regression(SIR)is an innovative and effective method for sufficient dimension reduction and data visualization.Recently,an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion.Nonetheless,few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view.To address this issue,we in this paper establish the min-imax rates of convergence for estimating the sparse SIR directions under various commonly used loss functions in the literature of sufficient dimension reduction.We also discover the possible trade-off between statistical and computational performance for sparse SIR.We finally propose an adaptive sparse SIR estimation scheme which is computationally tractable and nearly approaching the optimal estimation rate.Simulation studies are car-ried out to confirm the theoretical properties of our proposed methods,real data examples are also used to illustrate effectiveness of the proposed methods.