Automatic diagonal loading for Tyler's robust covariance estimator

An approach of regularizing Tyler's robust M-estimator of the co-variance matrix is proposed. We also provide an automatic choice of the regularization parameter in the high-dimensional regime. Simulations show its advantage over the sample covariance estimator and Tyler's M-estimator when data is heavy-tailed and the number of samples is small. Compared with the previous approaches of regularizing Tyler's M-estimator, our approach has a similar performance and a much simpler way of choosing the regularization parameter automatically.