Central subspaces review: methods and applications

doi:10.1214/22-SS138

Central subspaces review: methods and applications

2022-01-01

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DOI：10.1214/22-SS138

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Abstract

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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 develop-ments. However, over the last few years and with the advancement of tech-nology, many statistical problems are now situated in the high dimensional setting where p > n. In this article we review the theory of central sub-spaces 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 cen-tral subspace framework for bioinformatics applications and show, using two distinct data sets, how this framework can be applied in practice.

Keywords:

Central subspaces

sufficient dimension reduction

dimension reduction subspaces

sliced inverse regression

bioinformatics

omics

Central subspaces review: methods and applications

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