Response dimension reduction for the conditional mean in multivariate regression

Jae Keun Yoo, R. Dennis Cook

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Sufficient dimension reduction methodologies in regression have been developed in the past decade, focusing mostly on predictors. Here, we propose a methodology to reduce the dimension of the response vector in multivariate regression, without loss of information about the conditional mean. The asymptotic distributions of dimension test statistics are chi-squared distributions, and an estimate of the dimension reduction subspace is asymptotically efficient. Moreover, the proposed methodology enables us to test response effects for the conditional mean. Properties of the proposed method are studied via simulation.

Original languageEnglish
Pages (from-to)334-343
Number of pages10
JournalComputational Statistics and Data Analysis
Issue number2
StatePublished - 15 Dec 2008

Bibliographical note

Funding Information:
The authors are grateful to the referees for many helpful comments. The second author was supported in part by National Science Foundation Grant DMS-0405360.


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