A Model-Free Test for Reduced Rank in Multivariate Regression

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On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, methodology): “For example, replace the conditional distribution of Y |X by that of Y|X to define SY|X; replace E(Y |X) by E(Y|X) to define SE(Y|X) (Cook and Setodji 2003); and replace E(Y k|X) by E(Y⊗k|X) to define SE(Y⊗k |X), where Y⊗k = Y ⊗· · ·⊗ Y is the k-fold tensor product of Y, .”
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).”
Moment-based dimension reduction for multivariate response regression (2006, methodology): “= Σ −1/2 X S (k) Y|Z which implies that there is no loss of generality in standardizing X to have mean zero and identity covariance matrix.”
On Directional Regression for Dimension Reduction (2007, methodology): “Algorithms are available in the literature for calculating the distribution of linear combination of independent χ21 ’s, such as the foregoing (see Field 1993; Bentler and Xie 2000; Cook and Setodji 2003).”
Sequential sufficient dimension reduction for large p, small n problems (2015, methodology): “Many methods have been developed for estimating such a subspace, for instance, Cook and Setodji (2003), Yin and Bura (2006) and Li et al. (2008).”