Title: Sparsity and the Possibility of Inference
Author(s): Peter J. Bickel and Donghui Yan
Pages: 1 -- 24
We discuss the importance of sparsity in the context of nonparametric regression and covariance matrix estimation. We point to low manifold dimension of the covariate vector as a possible important feature of sparsity, recall an estimate of dimension due to Levina and Bickel (2005) and establish some conjectures made in that paper.