Refereed journal article or data article (A1)
Sliced Inverse Regression in Metric Spaces
List of Authors: Virta Joni, Lee Kuang-Yao, Li Lexin
Publisher: STATISTICA SINICA
Publication year: 2022
Journal: Statistica Sinica
Journal name in source: STATISTICA SINICA
Journal acronym: STAT SINICA
Volume number: 32
Issue number: SI
Start page: 2315
End page: 2337
Number of pages: 23
ISSN: 1017-0405
eISSN: 1996-8507
DOI: http://dx.doi.org/10.5705/ss.202022.0097
URL: https://www3.stat.sinica.edu.tw/statistica/j32n31/J32n3102/J32n3102.html
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/176797275
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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