Sufficient dimension reduction and graphics in regression

Abstract

In this article, we review, consolidate and extend a theory for sufficient dimension reduction in regression settings. This theory provides a powerful context for the construction, characterization and interpretation of low-dimensional displays of the data, and allows us to turn graphics into a consistent and theoretically motivated methodological body. In this spirit, we propose an iterative graphical procedure for estimating the meta-parameter which lies at the core of sufficient dimension reduction; namely, the central dimension-reduction subspace.