Abstract: 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 kth-moment weighted partial least squares to handle with the estimation of the central k th-conditional moment subspace. Finally, we obtain strong consistency