Optimal sufficient dimension reduction for the conditional mean in multivariate regression

Jae Keun Yoo, R. Dennis Cook

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


The aim of this article is to develop optimal sufficient dimension reduction methodology for the conditional mean in multivariate regression. The context is roughly the same as that of a related method by Cook & Setodji (2003), but the new method has several advantages. It is asymptotically optimal in the sense described herein and its test statistic for dimension always has a chi-squared distribution asymptotically under the null hypothesis. Additionally, the optimal method allows tests of predictor effects. A comparison of the two methods is provided.

Original languageEnglish (US)
Pages (from-to)231-242
Number of pages12
Issue number1
StatePublished - Mar 2007

Bibliographical note

Funding Information:
ACKNOWLEDGEMENT The authors are grateful to the referees for many helpful comments. This work was supported in part by grants from the U.S. National Science Foundation.


  • Multivariate conditional mean
  • Multivariate regression
  • Predictor effect test
  • Sufficient dimension reduction


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