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Biometrika Advance Access published online on February 7, 2007
Biometrika, doi:10.1093/biomet/asm003
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Copyright © Biometrika Trust

Optimal sufficient dimension reduction for the conditional mean in multivariate regression

Jae Keun Yoo and Dennis R. Cook

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


  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


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