Sequential and simultaneous distance-based dimension reduction

This paper introduces a method called Sequential and Simultaneous Distance-based Dimension Reduction (S2D2R) that performs simultaneous dimension reduction for a pair of random vectors based on distance covariance (dCov). Compared with sufficient dimension reduction (SDR) and canonical correlation analysis (CCA)-based approaches, S2D2R is a model-free approach that does not impose dimensional or distributional restrictions on variables and is more sensitive to nonlinear relationships. Theoretically, we establish a non-asymptotic error bound to guarantee the performance of S2D2R. Numerically, S2D2R performs comparable to or better than other state-of-the-art algorithms and is computationally faster. All codes of our S2D2R method can be found on GitHub https://github.com/Yijin911/S2D2R.git, including an R package named S2D2R.