Moment-based dimension reduction for multivariate response regression

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On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, methodology): “Next, we compare PR with four existing methods for multivariate-response dimension reduction estimators, which are marginal combination (MC), multivariate slicing (MS), and the two moment methods introduced by Yin and Bura (2005), which will be denoted by YB1 and YB2.”
Kernel dimension reduction in regression (2009, methodology): “e [7]. The general problem in these cases is that the estimated subspace is smaller than the central subspace. One approach to tackling these limitations is to incorporate higher-order moments of Y|X [34], but in practice the gains achievable by the use of higher-order moments are limited by robustn”
Nonlinear sufficient dimension reduction for functional data (2017, background): “The situation where Y is also a vector was considered in Cook and Setodji (2003), Yin and Bura (2006) and Li, Wen and Zhu (2008).”