Regularized robust estimation of mean and covariance matrix under heavy tails and outliers

In this paper we consider the regularized mean and covariance estimation problem for samples drawn from elliptical family of distributions. The proposed estimator yields robust estimates when the underlying distribution is heavy-tailed or when there are outliers in the data samples. In the scenario that the number of samples is small, it shrinks the estimator of the mean and covariance towards arbitrary given prior targets. Numerical algorithms are designed for the estimator based on the majorization-minimization framework and the simulation shows that the proposed estimator achieves considerably better performance.