Many sufficient dimension reduction methods for univariate regression have been extended to multivariate regression. Sliced average variance estimation (SAVE) has the potential to recover more reductive information and recent development enables us to test the dimension and predictor effects with distributions commonly used in the literature. In this paper, we aim to extend the functionality of the SAVE to multivariate regression. Toward the goal, we propose three new methods. Numerical studies and real data analysis demonstrate that the proposed methods perform well.
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Acknowledgements For the corresponding author Jae Keun Yoo, this work was partially supported by the Ewha Womans University Research Grant of 2010 and was supported by Basic Science Research Program through the National Research Foundation of Korea (KRF) funded by the Ministry of Education, Science and Technology (2010-0003189). The authors are grateful to the referees for many helpful comments.
- Double slicing
- K-means clustering
- Multivariatere gression
- Pooled estimation
- Sliced average variance estimation