Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are set in a general parametric or semiparametric framework.

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...</citationref>