Chi-squared tests in kth-moment sufficient dimension reduction

Abstract

We present a novel approach to sufficient dimension reduction for the conditional kth moments in regression. The approach provides a computationally feasible test for the dimension of the central kth-moment subspace. In addition, we can test predictor effects without assuming any models. All test statistics proposed in the novel approach have asymptotic chi-squared distributions.

Keywords:

• chi-squared tests
• kth-moment dimension reduction
• predictor effect tests
• regression
• sufficient dimension reduction

AMS Subject Classifications: :

• 62G08
• 62H05

Acknowledgements

This work was supported by Basic Science Research Programme through the National Research Foundation of Korea (KRF) funded by the Ministry of Education, Science and Technology (2011-0005581). The author is grateful to the referees for many helpful comments.