Weight fused functional sliced average variance estimation

Abstract

Selecting the number of slice is a key step for the implement of the sliced average variance estimation (SAVE) method. To our knowledge, there is no widely accepted method for it in a practical application. And an incorrect number of the slice may leads to an inaccurate conclusion. In traditional multivariate sufficient dimension reduction procedure, it is usually to adopt the fuze approach which combined the kernel operators of SAVE with various numbers of slices to solve this problem. Due to the infinite dimension in functional data, the fuze approach can not be directly applied to functional SAVE (FSAVE). Hence we propose a novel fused approach which based on a weighted kernel operator of FSAVE that named as the approach weight fused FSAVE (WFFSAVE). Simulation studies show that the WFFSAVE method performs better than FSAVE. And we also apply this new method to the Tecator data set.