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Asymptotically Linear Estimators of the Precision Matrix

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Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 2159)

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

Keywords

  • Tuning Parameter
  • Severe Restriction
  • Normal Estimator
  • Positive Definite Matrix
  • Linear Estimator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 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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