# Estimation of functionals of sparse covariance matrices

arXiv: https://arxiv.org/abs/1408.5087 · HTML: https://mlsanity.com/paper/1408.5087/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Aug 2014.

## Built on by (most cited first, 2 of 2)

- [Covariance alignment: from maximum likelihood estimation to Gromov-Wasserstein](https://mlsanity.com/paper/2311.13595/) (2023)
- [Precise sample covariance spectral norm error -- an RDT view](https://mlsanity.com/paper/2607.14460/) (2026)

## Abstract (arXiv)

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other ℓr norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Akin to previous results on functional estimation, the minimax rates exhibit an elbow phenomenon. Our results are further illustrated in simulated data as well as an empirical study of data arising in financial econometrics.