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Bridging linearity-based and kernel-based sufficient dimension reduction (2010.15009v1)
Published 28 Oct 2020 in stat.ME, math.ST, and stat.TH
Abstract: There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite functions to link linear SDR procedures to their nonlinear counterparts.
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