An RKHS formulation of the inverse regression dimension-reduction problem
The Annals of Statistics · 2009 · Volume 37 · Issue 2
Abstract
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 ξ1, …, ξp which belong to the closed span LX2 of X. This paper investigates a unified framework for the inverse regression dimension-reduction problem. It is found that the identification of LX2 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.
Keywords
62H99, 62M99, Functional data analysis, sliced inverse regression
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