# Confidence intervals for high-dimensional inverse covariance estimation

arXiv: https://arxiv.org/abs/1403.6752 · HTML: https://mlsanity.com/paper/1403.6752/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2014.

## Built on by (most cited first, 7 of 7)

- [Debiased Machine Learning without Sample-Splitting for Stable Estimators](https://mlsanity.com/paper/2206.01825/) (2022)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [Inference on Optimal Dynamic Policies via Softmax Approximation](https://mlsanity.com/paper/2303.04416/) (2023)
- [On confidence intervals for precision matrices and the eigendecomposition of covariance matrices](https://mlsanity.com/paper/2208.11977/) (2022)
- [Inference for High-Dimensional Sparse Spectral Precision Matrices](https://mlsanity.com/paper/2606.07986/) (2026)
- [High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series](https://mlsanity.com/paper/2609.30565/) (2026)

## Abstract (arXiv)

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian limiting distribution. Asymptotic properties of the novel estimator are analyzed for the case of sub-Gaussian observations under a sparsity assumption on the entries of the true precision matrix and regularity conditions. Thresholding the de-sparsified estimator gives guarantees for edge selection in the associated graphical model. Performance of the proposed method is illustrated in a simulation study.