Projective-resampling minimum average variance estimation for multivariate regression

This paper addresses the challenge of dimension reduction for a multivariate regression. We introduce a novel approach that integrates the minimum average variance estimation (Xia et al., 2002) with the projective resampling approach (Li et al., 2008) to render its applicability in multivariate response settings. By applying the minimum average variance estimation within the projective resampling framework, we achieve an effective dimension reduction, ensuring the exhaustive recovery of the central mean subspace and eradicating strong assumptions on the distribution of predictors. The proposed methodology is validated through intensive numerical studies to evaluate its effectiveness and robustness in various multivariate regressions. Further refinement made improves the computational performance as well.