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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 231-242 |
| Number of pages | 12 |
| Journal | Biometrika |
| Volume | 94 |
| Issue number | 1 |
| DOIs | |
| State | Published - 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.
Keywords
- Multivariate conditional mean
- Multivariate regression
- Predictor effect test
- Sufficient dimension reduction