  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.
