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An RKHS formulation of the inverse regression dimension-reduction problem. (English) Zbl 1162.62053
Summary: 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 \(\xi _{1}, \dots , \xi _p\) 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 convenient computational algorithms that can be applied to a variety of models.

62H12 Estimation in multivariate analysis
62M99 Inference from stochastic processes
46N30 Applications of functional analysis in probability theory and statistics
62H99 Multivariate analysis
62J99 Linear inference, regression
65C60 Computational problems in statistics (MSC2010)
fda (R); gss
Full Text: DOI arXiv
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