High-dimensional regression analysis with treatment comparisons

We consider the treatment comparison problem in a general high-dimensional regression setting. In this article, we propose a nonparametric estimation approach based on partial sliced inverse regression (SIR) (Chiaromonte et al. in Ann Stat 30:475–497, <CitationRef CitationID="CR4">2002</CitationRef>) and an extension of partial inverse mean matching (Carroll and Li in Stat Sin 5:667–688, <CitationRef CitationID="CR2">1995</CitationRef>) without requiring a prespecified parametric model. A sparse estimation strategy is incorporated in our approach to enhance the interpretation of variable selection. Several simulation examples are used to compare our method with SIR and principal components analysis. Illustrative applications to two real datasets are also presented. Copyright Springer-Verlag 2013