Sufficient dimension folding in regression via distance covariance for matrix-valued predictors

In modern data, when predictors are matrix/array-valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model-free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we propose a new method of local search to estimate the structural dimensions. Simulations and real data analysis support the efficiency and effectiveness of the proposed method.