# Linear shrinkage of sample covariance matrix or matrices under elliptical distributions: a review

arXiv: https://arxiv.org/abs/2308.04721 · HTML: https://mlsanity.com/paper/2308.04721/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2023.

## Built on by (most cited first, 1 of 1)

- [ITC-MoE: Importance-guided Token-aware Compression for MoE Diffusion Language Models](https://mlsanity.com/paper/2610.01296/) (2026)

## Abstract (arXiv)

This chapter reviews methods for linear shrinkage of the sample covariance matrix (SCM) and matrices (SCM-s) under elliptical distributions in single and multiple populations settings, respectively. In the single sample setting a popular linear shrinkage estimator is defined as a linear combination of the sample covariance matrix (SCM) with a scaled identity matrix. The optimal shrinkage coefficients minimizing the mean squared error (MSE) under elliptical sampling are shown to be functions of few key parameters only, such as elliptical kurtosis and sphericity parameter. Similar results and estimators are derived for multiple population setting and applications of the studied shrinkage estimators are illustrated in portfolio optimization.