Multivariate response directional regression: a projective resampling approach

In high dimensional data analysis, directional regression is a widely used method for implementing linear sufficient dimension reduction by extracting core information from the complex data structure. However, extending sufficient dimension reduction techniques to handle multivariate response data remains a relatively challenging task. In this paper, we propose a novel method that integrates directional regression with the projective resampling framework to tackle the multivariate response regression problem. Our method, called projective resampling directional regression, not only improves estimation accuracy of the dimension reduction subspace but also offers greater flexibility of directional regression across diverse datasets. We establish theoretical properties of our method, including consistency and convergence rates. Comprehensive simulation studies under various scenarios, along with analyses of two real-world datasets, demonstrate the effectiveness and competitiveness of our approach.