Abstract
This chapter looks at two approaches towards establishing confidence intervals for the entries in high-dimensional precision matrix. The first approach is based on the graphical Lasso, whereas the second one invokes the square-root node-wise Lasso as initial estimator. In both cases the one-step adjustment or “de-sparsifying step” is numerically very simple. Under distributional and sparsity assumptions, the de-sparsified estimator of the precision matrix is asymptotically linear. Here, the conditions are stronger when using the graphical Lasso than when using the square-root node-wise Lasso
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Notes
- 1.
This can be generalized to sub-Gaussian data.
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van de Geer, S. (2016). Asymptotically Linear Estimators of the Precision Matrix. In: Estimation and Testing Under Sparsity. Lecture Notes in Mathematics(), vol 2159. Springer, Cham. https://doi.org/10.1007/978-3-319-32774-7_14
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DOI: https://doi.org/10.1007/978-3-319-32774-7_14
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