Title: Asymptotic Confidence Regions for High-dimensional Structured Sparsity,
Abstract: In the setting of high-dimensional linear regression models, we propose two
frameworks for constructing pointwise and group confidence sets for penalized
estimators which incorporate prior knowledge about the organization of the
non-zero coefficients. This is done by desparsifying the estimator as in van de
Geer et al. [18] and van de Geer and Stucky [17], then using an appropriate
estimator for the precision matrix $\Theta$. In order to estimate the precision
matrix a corresponding structured matrix norm penalty has to be introduced.
After normalization the result is an asymptotic pivot.
The asymptotic behavior is studied and simulations are added to study the
differences between the two schemes.