Title: Sparsity and the Possibility of Inference

Author(s): Peter J. Bickel and Donghui Yan
Issue: Volume 70 Series A Part 1 Year 2008
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.
AMS (2000) subject classification. Primary 62-02, 62G08, 62G20, 62J10.
Keywords and phrases: Sparsity, statistical inference, nonparametric regression, covariance matrix estimation, dimension estimation.