An asymptotic result for sliced inverse regression (Q1966009)

The author considers the model \( Y=m(\beta_1^TX,...,\beta_K^TX,\varepsilon)\) where \(K,\;1 \leq K\leq d,\) and \(m:R^{K+1} \to R\) are unknown. In this model \(Y\) is a random variable, \(X\) is an \(R^d\) random vector, and \(\varepsilon\) is a noise random variable. Sliced inverse regression considers inverse regression whose aim is to estimate \(E[X |Y=y].\) This method reduces the regressor space to a lower dimension where nonparametric regression can be applied. Algorithms for sliced inverse regression are given. Asymptotic statistical properties are considered, and some applications of sliced inverse regression are shown.