A New RKHS-based Genernlized Semiparametric Approach To Nonlinear Dimension Reduction

In recent years, big data has become a hot spot in many research areas, such as news intelligent push, financial, machine learning etc. Dealing with the big data is not easy especially with the high dimensional data since we have to face the curse of dimensionality. So how to effectively extract the interested information from high dimensional data still is a big challenge in statistical re-search. Dimension reduction is one of the important and effective methods to deal with high dimensional data, especially when the data is sparse. According to the theory of semiparamctric and reproducing kernel Hilbert space(RKHS), a novel approach named generalised semiparametric kernel sliced inverse regression (GSKSIR) is proposed to solve the nonlinear dimension-reduction problem.To the best of our knowledge the current paper is the first work to generalize the semi-parametric model to generalized semiparametric model which allows both the interesting parameters and nuisance parameters to be infinite dimensional. In a semiparametirc framework we calculate the orthogonal complement space of gen-eralized nuisance tangent space to derive the estimating equation. Solving the estimating equation by the theory of RKHS and regularization, we obtain the estimation of dimension reduction directions of the sufficient dimension reduction (SDR) subspace.Simulation studies are conducted to demonstrate the finite sam-ple performance of our method in comparison with several existing methods.