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math.ST2023
Functional Slicing-free Inverse Regression via Martingale Difference Divergence Operator
Songtao Tian, Zixiong Yu, Rui Chen
Functional sliced inverse regression (FSIR) is one of the most popular algorithms for functional sufficient dimension reduction (FSDR). However, the choice of slice scheme in FSIR…
math.ST2023
On the Optimality of Functional Sliced Inverse Regression
Rui Chen, Songtao Tian, Dongming Huang +2
In this paper, we prove that functional sliced inverse regression (FSIR) achieves the optimal (minimax) rate for estimating the central space in functional sufficient dimension red…
math.ST2023
On the Structural Dimension of Sliced Inverse Regression
Dongming Huang, Songtao Tian, Qian Lin
In this work, we address the longstanding puzzle that Sliced Inverse Regression (SIR) often performs poorly for sufficient dimension reduction when the structural dimension (th…