2. Inverse mean difference approach
Let Y be a response variable in a regression problem and X be a p dimensional predictor vector, where for simplicity we
assume E(X) = 0. Let n be the number of observations in our regression problem and H the number of slices.
Sliced inverse regression (SIR) by Li (1991) uses the idea of the inverse first moment to estimate the CS. More specifically
a spectral decomposition of (6)−1var(E(X|Y)) is used where 6 = var(X). More recently Zhu et al.