已有降维方法的推广

Generalization of Some Dimension Reduction Methods

SAVE,PHD和SIR_(Ⅱ)已被证明是有效的降维方法,这些方法基于下面的两个假设:线性条件和常数方差条件.但是,常数方差条件非常强.当常数方差不成立时,即使线性条件成立,SAVE,PHD和SIR_(Ⅱ)经常会找到中心空间之外的方向.通过去掉了常数方差条件,在较弱条件下推广了SAVE,PHD和SIR_(Ⅱ).从而使得在较弱的条件下,能得到中心空间的正确估计.

SAVE, PHD and SIRII are proven effective methods in dimension reduction problems. These methods are based on two assumptions： linearity condition and constant covariance condition. However, constant covariance condition is very strict. In the situation where constant covariance condition fails, even if linearity condition holds, SAVE, PHD and SIRII often pick the directions which are outside of the CS. This paper removes the constant covariance condition and generalize SAVE, PHD and SIRII under weaker conditions. This generalization makes it possible to get the correct estimates of CS under weaker condition. Simulation results are reported.