Refereed journal article or data article (A1)

Sliced Inverse Regression in Metric Spaces

List of AuthorsVirta Joni, Lee Kuang-Yao, Li Lexin


Publication year2022

JournalStatistica Sinica

Journal name in sourceSTATISTICA SINICA

Journal acronymSTAT SINICA

Volume number32

Issue numberSI

Start page2315

End page2337

Number of pages23





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In this article, we propose a general nonlinear sufficient dimension reduc-tion (SDR) framework when both the predictor and the response lie in some general metric spaces. We construct reproducing kernel Hilbert spaces with kernels that are fully determined by the distance functions of the metric spaces, and then leverage the inherent structures of these spaces to define a nonlinear SDR framework. We adapt the classical sliced inverse regression within this framework for the metric space data. Next we build an estimator based on the corresponding linear opera-tors, and show that it recovers the regression information in an unbiased manner. We derive the estimator at both the operator level and under a coordinate system, and establish its convergence rate. Lastly, we illustrate the proposed method using synthetic and real data sets that exhibit non-Euclidean geometry.

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Last updated on 2023-13-01 at 15:52