### Abstract

We extend to the matrix setting a recent result of Srivastava-Vershynin [24] about estimating the covariance matrix of a random vector. The result can be interpreted as a quantified version of the law of large numbers for positive semi-definite matrices which verify some regularity assumption. Beside giving examples, we discuss the notion of log-concave matrices and give estimates on the smallest and largest eigenvalues of a sum of such matrices.

Original language | English (US) |
---|---|

Article number | 107 |

Journal | Electronic Journal of Probability |

Volume | 18 |

DOIs | |

State | Published - Dec 19 2013 |

### Keywords

- Covariance matrix
- Log-concave matrix

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'Estimating the covariance of random matrices'. Together they form a unique fingerprint.

## Cite this

Youssef, P. (2013). Estimating the covariance of random matrices.

*Electronic Journal of Probability*,*18*, [107]. https://doi.org/10.1214/EJP.v18-2579