The hybrid method of FSIR and FSAVE for functional effective dimension reduction

Functional Sliced Inverse Regression (FSIR) and Functional Sliced Average Variance Estimation (FSAVE) are two popular functional effective dimension reduction methods. However, both of them have restrictions: FSIR is vulnerable to symmetric dependencies and FSAVE has low efficiency for monotone dependencies and is sensitive to the number of slices. To avoid aforementioned disadvantages, a hybrid method of FSIR and FSAVE is developed. Theoretical properties for the hybrid method and the consistency result of the proposed hybrid estimator are derived. Simulation studies show that the hybrid method has better performance than those of FSIR and FSAVE. The proposed method is also applied on the Tecator data set.