A Multiple-Index Model and Dimension Reduction

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On estimation efficiency of the central mean subspace (2014, background): “When β contains more than one column, it is sometimes also referred to as a multi-index model (Xia et al., 2002; Xia, 2008).”
A Simple Two-Sample Test in High Dimensions Based on L2-Norm (2020, background): “In regression, feature screening and selection, and dimension reduction are the mainstream approaches (Cheng and Wu 2013; Cook and Li 2002; Fan and Li 2001; Fan and Lv 2008; Fan and Peng 2004; Fan and Song 2010; Lv and Fan 2009; Li et al. 2012; Tibshirani 1996; Xia 2007, 2008).”
A Semiparametric Approach to Interpretable Machine Learning (2020, methodology): “The models we use in this simulation study belong to the class of multiple-index models [44, 15], a flexible class of models that represent common models such as the partially linear model [37, 40] and the single index model [15].”