Dimension reduction for the conditionalkth moment in regression

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2002 · Volume 64 · Issue 2

Abstract

The idea of dimension reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a prespecified model. Central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction. Here, we introduce the centralkth-moment subspace to capture information from the mean, variance and so on up to thekth conditional moment of the regression. New methods are studied for estimating these subspaces. Connections with sliced inverse regression are established, and examples illustrating the theory are presented.

Keywords

Central subspaces, Dimension reduction subspaces, Permutation tests, Regression graphics, Sliced inverse regression

Enable JavaScript for citation tools and additional paper interactions.