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Biometrika Advance Access originally published online on February 7, 2007
Biometrika 2007 94(1):231-242; doi:10.1093/biomet/asm003
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Copyright © 2007 Biometrika Trust

Articles

Optimal sufficient dimension reduction for the conditional mean in multivariate regression

Jae Keun Yoo

Department of Bioinformatics and Biostatistics, School of Public and Information Sciences, University of Louisville, 555 S. Floyd Street, Louisville, Kentucky 40292, U.S.A.

R. Dennis Cook

School of Statistics, University of Minnesota, 224 Church Street S.E. Minneapolis, Minnesota 55455, U.S.A.

peter.yoo{at}louisville.edu

dennis{at}stat.umn.edu

Received for publication 1 October 2005. Revision received 1 May 2006.
  Abstract

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.

Key Words: multivariate conditional mean • multivariate regression • predictor effect test • sufficient dimension reduction

The originally published version of this article was incorrect. The full text version of the article was incorrectly displayed. The publisher apologizes for this error.


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