# Asymptotic Performance of Complex M-estimators for Multivariate Location and Scatter Estimation

## TL;DR

This paper derives the asymptotic performance of complex M-estimators for multivariate location and scatter estimation, addressing robustness issues in multivariate analysis, especially in complex data scenarios.

## Contribution

It extends the asymptotic analysis of M-estimators from real to complex cases, providing theoretical insights into their performance.

## Key findings

- Asymptotic performance formulas derived for complex M-estimators
- Addresses robustness against outliers in complex multivariate data
- Enhances understanding of complex estimator behavior in high-dimensional settings

## Abstract

The joint estimation of means and scatter matrices is often a core problem in multivariate analysis. In order to overcome robustness issues, such as outliers from Gaussian assumption, M-estimators are now preferred to the traditional sample mean and sample covariance matrix. These estimators are well established and studied in the real case since the seventies. Their extension to the complex case has drawn recent interest. In this letter, we derive the asymptotic performance of complex M-estimators for multivariate location and scatter matrix estimation.