A selective review of sufficient dimension reduction for multivariate response regression

TL;DR

This paper provides a comprehensive review of various sufficient dimension reduction methods for multivariate response regression, categorizing them into inverse and forward regression estimators and discussing their characteristics.

Contribution

It offers a structured overview of SDR estimators, highlighting the distinctions and specific types within inverse and forward regression frameworks.

Findings

Classifies SDR estimators into inverse and forward regression categories.

Describes specific methods such as pooled marginal, projective resampling, and distance-based estimators.

Discusses estimators like OLS, PLS, and semiparametric SDR within the forward regression family.

Abstract

We review sufficient dimension reduction (SDR) estimators with multivariate response in this paper. A wide range of SDR methods are characterized as inverse regression SDR estimators or forward regression SDR estimators. The inverse regression family include pooled marginal estimators, projective resampling 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.