The Annals of Statistics
- Ann. Statist.
- Volume 37, Number 2 (2009), 726-755.
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 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.
Ann. Statist., Volume 37, Number 2 (2009), 726-755.
First available in Project Euclid: 10 March 2009
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Hsing, Tailen; Ren, Haobo. An RKHS formulation of the inverse regression dimension-reduction problem. Ann. Statist. 37 (2009), no. 2, 726--755. doi:10.1214/07-AOS589. https://projecteuclid.org/euclid.aos/1236693148