Estimating central subspaces via inverse third moments

Xiangrong Yin, R. Dennis Cook

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

Modern graphical tools have enhanced our ability to learn many things from data directly. In recent years, dimension reduction has proven to be an effective tool for generating low-dimensional summary plots without appreciable loss of information. Some well-known inverse regression methods for dimension reduction such as sliced inverse regression (Li, 1991) and sliced average variance estimation (Cook & Weisberg, 1991) have been developed to estimate summary plots for regression and discriminant analysis. In this paper, we suggest a new method that makes use of inverse third moments. This method can find structure beyond that found by sliced inverse regression and sliced average variance estimation, particularly regression mixtures. Illustrative examples are presented.

Original languageEnglish (US)
Pages (from-to)113-125
Number of pages13
JournalBiometrika
Volume90
Issue number1
DOIs
StatePublished - Mar 2003

Bibliographical note

Funding Information:
The authors would like to thank the editor, the associate editor and referees whose suggestions led to a greatly improved paper. The work of Yin was supported in part by the University of Georgia Research Foundation and the work of Cook was supported in part by grants from the U.S. National Science Foundation.

Keywords

  • Central subspace
  • Dimension-reduction subspace
  • Inverse regression method
  • Regression graphics

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