Using intraslice covariances for improved estimation of the central subspace in regression

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On estimation efficiency of the central mean subspace (2014, methodology): “Following the idea of Cook and Ni (2005, 2006), Yoo and Cook (2007) proposed weighted alternating least squares to improve the usual ordinary least squares estimator when Y is multivariate.”
Principal fitted components for dimension reduction in regression (2008, background): “While this information might be recovered by intra slice fitting (Cook and Ni, 2006), we expect that PFC modeling is not as prone to such information loss.”
Dimension reduction for nonelliptically distributed predictors (2009, methodology): “The loss of intra-slice information by SIR is noticed by Cook and Ni (2006), who proposed a method to reduce it.”
Sliced Regression for Dimension Reduction (2008, methodology): “Although slicing can help us in discovering the complicated CS structure, it may also leads to information loss (Cook and Ni, 2006).”
Shrinkage inverse regression estimation for model‐free variable selection (2009, methodology): “Keywords: Inverse regression estimation; Non-negative garrotte; Sliced inverse regression; Sufficient dimension reduction; Variable selection”