An RKHS formulation of the inverse regression dimension-reduction problem

Suppose that Y is a scalar and X is a second-order stochastic process, where Y and X are conditionally independent given the random variables xi(1), ..., xi(p) which belong to the closed span L-X(2) of X. This paper investigates a unified framework for the inverse regression dimension-reduction problem. It is found that the identification of L-X(2) with the reproducing kernel Hilbert space of X provides a platform for a seamless extension from the finite- to infinite-dimensional settings. It also facilitates convenient computational algorithms that can be applied to a variety of models.