Central subspaces review: methods and applications

Sabrina A. Rodrigues, Richard Huggins, Benoit Liquet

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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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 p ≤ n, 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.

Original languageEnglish
Pages (from-to)210-237
Number of pages28
JournalStatistics Surveys
Publication statusPublished - 2022

Bibliographical note

Copyright © 2022, Institute of Mathematical Statistics. All rights reserved. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • bioinformatics
  • Central subspaces
  • dimension reduction subspaces
  • omics
  • sliced inverse regression
  • sufficient dimension reduction


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