A novel moment-based sufficient dimension reduction approach in multivariate regression

Recently, a moment-based sufficient dimension reduction methodology in multivariate regression, focusing on the first two moments, was introduced. We present in this article a novel approach of the earlier method in roughly the same context. This novel method possesses several desirable properties that the earlier method did not have such as dimension tests with chi-squared distributions, predictor effects test without assuming any model, and so on. Simulated and real data examples are presented for studying various properties of the proposed method and for a numerical comparison to the earlier method.