## Abstract

We study the behavior of Maronna's robust scatter estimator Cˆ_{N}∈C^{N×N} built from a sequence of observations y_{1},…,y_{n} lying in a K-dimensional signal subspace of theN-dimensional complex field corrupted by heavy tailed noise, i.e., y_{i}=A_{N}s_{i}+x_{i}, where A_{N}∈C^{N×K} and x_{i} is drawn from an elliptical distribution. In particular, we prove under mild assumptions that the robust scatter matrix can be characterized by a random matrix Sˆ_{N} that follows a standard random model as the population dimension N, the number of observations n, and the rank of A_{N} grow to infinity at the same rate. Our results are of potential interest for statistical theory and signal processing.

Original language | English (US) |
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Pages (from-to) | 51-70 |

Number of pages | 20 |

Journal | JOURNAL OF MULTIVARIATE ANALYSIS |

Volume | 162 |

DOIs | |

State | Published - Nov 2017 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2017 Elsevier Inc.

## Keywords

- Random matrix theory
- Robust scatter estimation
- Robust statistics
- Signal plus noise model

## ASJC Scopus subject areas

- Numerical Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty