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We review sufficient dimension reduction (SDR) estimators with multivariateresponse in this paper. A wide range of SDR methods are characterized asinverse regression SDR estimators or forward regression SDR estimators. Theinverse regression family include pooled marginal estimators, projectiveresampling estimators, and distance-based estimators. Ordinary least squares,partial least squares, and semiparametric SDR estimators, on the other hand,are discussed as estimators from the forward regression family.

A selective review of sufficient dimension reduction for multivariate response regression