Title: Sufficient dimension folding in regression via distance covariance for matrix-valued predictors
Authors: Wenhui Sheng - Marquette University (United States) [presenting]
Abstract: In modern data, when predictors are matrix/array-valued, building a reasonable model is much more difficult due to the complicated structure. However, dimension folding that reduces the predictor dimensions while keeping its structure is critical in helping to build a useful model. 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 the 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.