M-Estimators of Scatter with Eigenvalue Shrinkage

Esa Ollila (1) , Daniel P. Palomar (2) , Frédéric Pascal (3)

1 School of Electrical Engineering [Aalto Univ]
2 HKUST - Hong Kong University of Science and Technology
3 L2S - Laboratoire des signaux et systèmes

A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigen-values toward its grand mean. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator of scatter matrix and a fully automatic data adap-tive method to compute the optimal shrinkage parameter with minimum mean squared error is proposed. Our approach permits the use of any weight function such as Gaussian, Hu-ber's, or t weight functions, all of which are commonly used in M-estimation framework. Our simulation examples illustrate that shrinkage M-estimators based on the proposed optimal tuning combined with robust weight function do not loose in performance to shrinkage SCM estimator when the data is Gaussian, but provide significantly improved performance when the data is sampled from a heavy-tailed distribution.

Keywords: M-estimators; sample covariance matrix; shrinkage; regularization; elliptical distributions

Domains: Signal and Image Processing; Other Statistics [stat.ML]; Applications [stat.AP]

Esa Ollila, Daniel P. Palomar, Frédéric Pascal. M-Estimators of Scatter with Eigenvalue Shrinkage. ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2020, Barcelone, Spain. pp.5305-5309, ⟨10.1109/ICASSP40776.2020.9054555⟩. ⟨hal-02591476⟩