Successive direction extraction for estimating the central subspace in a multiple-index regression

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Dimension reduction for nonelliptically distributed predictors (2009, methodology): “The similar problem arises frequently in dimension reduction; for example, it arises also in Xia et al. (2002), Cook and Ni (2005) and Cook (2007).”
On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, methodology): “The second category includes the minimum average variance estimator of Xia et al. (2002) and the information index method of Yin and Cook (2005) and Yin, Li, and Cook (2008).”
Sufficient Dimension Reduction via Distance Covariance (2016, methodology): “An alternative procedure suggested by a referee is to use a successive one-at-a-time search similar to that of Yin, Li, and Cook (2008).”
Groupwise Dimension Reduction (2010, background): “Recently, Yin, Li, and Cook (2008) gave a very mild sufficient condition for this implication to hold.”