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.

摘要

切片数量的选择是切片平均方差估计（SAVE）方法实现的关键步骤。据我们所知，在实际应用中没有被广泛接受的方法。并且不正确的切片数可能导致不准确的结论。在传统的多元充分降维过程中，通常采用将SAVE的核算子与不同数量的切片相结合的引信方法来解决这个问题。由于功能数据的无限维，引信方法不能直接应用于功能保存（FSAVE）。因此，我们提出了一种新的融合方法，它基于 FSAVE 的加权核算子，称为方法权重融合 FSAVE (WFFSAVE)。模拟研究表明，WFFSAVE 方法的性能优于 FSAVE。