The conditional mean, variance and higher-conditional
moment functions are often of special interest in regression. In
this paper,we generalize central mean subspace and focus especial
attention on the k th-conditional moment function. For this, we
first borrow the new concept --- the central k th-conditional
moment subspace, and study its basic properties. To avoid computing
the inverse of the covariance of predictors with large
dimensionality and highly collinearity, we develop a method called
the $k$th-moment weighted partial least squares to handle with the
estimation of the central k th-conditional moment subspace.
Finally, we obtain strong consistency