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Abstract |
This paper proposes a nonlinear dimension reduction method - the generalized semiparametric kernel sliced inverse regression (GSKSIR for short), developed based on the theory of reproducing kernel Hilbert Space (RKHS) and the semiparametric method.
This method extends the classical semiparametric method into more generalized semiparametric domain, and is capable of handling infinite dimensional interested parameter spaces. Under this method, both spaces of nuisance parameters and parameters of interests can be infinite dimensional, the corresponding generalized nuisance tangent space orthogonal complement is derived, estimation equation for the purpose of dimension reduction is constructed, and optimization of the target function can be achieved based on RKHS theory and regularization method, which leads to a nonlinear estimated sufficient reduced dimension subspace with efficient properties. Furthermore, this new method does not impose the linearity design conditions (LDC) under methods such as the sliced inverse regression (SIR) and the kernel SIR, and so on, and thus, is more general and can be more widely applied.
Finally, a Monte Carlo simulation is conducted, the results demonstrate the excellent finite sample properties of this new method. |
