Asymptotic Confidence Regions for High-Dimensional Structured Sparsity - 2018


In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and cluster confidence sets for penalized estimators, that incorporate prior information about the organization of the nonzero coefficients. This is often done by desparsifying the estimator by S. van de Geer and B. Stucky and S. van de Geer et al., then using an applicable estimator for the precision matrix T. In order to estimate the precision matrix a corresponding structured matrix norm penalty has got to be introduced. After normalization the result's an asymptotic pivot. The asymptotic behavior is studied and simulations are added to review the differences between the 2 schemes.

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