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arXiv · 0904.0076

An RKHS formulation of the inverse regression dimension-reduction problem

Tailen Hsing·Haobo Ren
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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 $ξ_1,...,ξ_p$ 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.

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Tailen Hsing, Haobo Ren. 2009-04-01. An RKHS formulation of the inverse regression dimension-reduction problem. https://doi.org/10.1214/07-aos589

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