Dimension reduction for the conditional kth moment in regression

Xiangrong Yin, R. D Cook

Research output: Contribution to journalArticlepeer-review

114 Scopus citations


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 central kth-moment subspace to capture information from the mean, variance and so on up to the kth 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.

Original languageEnglish (US)
Pages (from-to)159-175
Number of pages17
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number2
StatePublished - 2002


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


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