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April 2009 An RKHS formulation of the inverse regression dimension-reduction problem
Tailen Hsing, Haobo Ren
Ann. Statist. 37(2): 726-755 (April 2009). DOI: 10.1214/07-AOS589

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.

Citation

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Tailen Hsing. Haobo Ren. "An RKHS formulation of the inverse regression dimension-reduction problem." Ann. Statist. 37 (2) 726 - 755, April 2009. https://doi.org/10.1214/07-AOS589

Information

Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62053
MathSciNet: MR2502649
Digital Object Identifier: 10.1214/07-AOS589

Subjects:
Primary: 62H99
Secondary: 62M99

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 2 • April 2009
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