M-estimators of scatter with eigenvalue shrinkage

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Journal Title
Journal ISSN
Volume Title
Conference article in proceedings
Date
2020-05
Major/Subject
Mcode
Degree programme
Language
en
Pages
5
5305-5309
Series
2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
Abstract
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 eigenvalues 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 adaptive 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, Huber'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.
Description
Keywords
Elliptical distributions, M-estimators, Regularization, Sample covariance matrix, Shrinkage
Other note
Citation
Ollila , E , Palomar , D P & Pascal , F 2020 , M-estimators of scatter with eigenvalue shrinkage . in 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings . , 9054555 , Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing , IEEE , pp. 5305-5309 , IEEE International Conference on Acoustics, Speech, and Signal Processing , Barcelona , Spain , 04/05/2020 . https://doi.org/10.1109/ICASSP40776.2020.9054555