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Activity Number:
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523
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Type:
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Invited
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Date/Time:
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Thursday, August 2, 2007 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #307806 |
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Title:
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An RKHS Formulation of the Inverse Regression Dimension Problem
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Author(s):
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Tailen Hsing*+ and Haobo Ren
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Companies:
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The Ohio State University and Alcatel-Lucent
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Address:
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Department of Statistics, Columbus, OH, 43210,
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Keywords:
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functional data ; nonparametric regression ; inverse regression ; reproducing kernel Hilbert space
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Abstract:
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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 $\xi_1,\ldots,\xi_p$ 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 a convenient computational algorithm that can be applied to a variety of models.
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