Sufficient dimension reduction and prediction through cumulative slicing PFC

In this article, a new method named cumulative slicing principle fitted component (CUPFC) model is proposed to conduct sufficient dimension reduction and prediction in regression. Based on the classical PFC methods, the CUPFC avoids selecting some parameters such as the specific basis function form or the number of slices in slicing estimation. We develop the estimator of the central subspace in the CUPFC method under three error-term structures and establish its consistency. The simulations investigate the effectiveness of the new method in prediction and reduction estimation with other competitors. The results indicate that the new proposed method generally outperforms the existing PFC methods no matter how the predictors are truly related to the response. The application to real data also verifies the validity of the proposed method.