Central subspaces review: methods and applications

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 $p\le n$, $p>n$ 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.