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2022 Central subspaces review: methods and applications
Sabrina A. Rodrigues, Richard Huggins, Benoit Liquet
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Statist. Surv. 16: 210-237 (2022). DOI: 10.1214/22-SS138

Abstract

Central subspaces have long been a key concept for sufficient dimension reduction. Initially constructed for solving problems in the p<n setting, central subspace methods have seen many successes and developments. However, over the last few years and with the advancement of technology, many statistical problems are now situated in the high dimensional setting where p>n. In this article we review the theory of central subspaces and give an updated overview of central subspace methods for the pn, p>n and big data settings. We also develop a new classification system for these techniques and list some R and MATLAB packages that can be used for estimating the central subspace. Finally, we develop a central subspace framework for bioinformatics applications and show, using two distinct data sets, how this framework can be applied in practice.

Acknowledgments

The authors sincerely thank the editor, the associate editor, and anonymous referees for their valuable comments that helped in improving the article significantly.

Citation

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Sabrina A. Rodrigues. Richard Huggins. Benoit Liquet. "Central subspaces review: methods and applications." Statist. Surv. 16 210 - 237, 2022. https://doi.org/10.1214/22-SS138

Information

Received: 1 April 2021; Published: 2022
First available in Project Euclid: 4 September 2022

Digital Object Identifier: 10.1214/22-SS138

Subjects:
Primary: 62P10 , 92B15

Keywords: Bioinformatics , Central subspaces , dimension reduction subspaces , omics , sliced inverse regression , sufficient dimension reduction

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Vol.16 • 2022
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