Spectral Shrinkage of Tyler's M -Estimator of Covariance Matrix - Archive ouverte HAL Access content directly
Conference Papers Year :

Spectral Shrinkage of Tyler's M -Estimator of Covariance Matrix

(1) , (2) , (3, 4)


Covariance matrices usually exhibit specific spectral structures, such as low-rank ones in the case of factor models. In order to exploit this prior knowledge in a robust estimation process, we propose a new regularized version of Tyler's M-estimator of covariance matrix. This estimator is expressed as the minimizer of a robust M-estimating cost function plus a penalty that is unitary invariant (i.e., that only applies on the eigenvalue) that shrinks the estimated spectrum toward a fixed target. The structure of the estimate is expressed through an interpretable fixed-point equation. A majorization-minimization (MM) algorithm is derived to compute this estimator, and the g-convexity of the objective is also discussed. Several simulation studies illustrate the interest of the approach and also explore a method to automatically choose the target spectrum through an auxiliary estimator.
Fichier principal
Vignette du fichier
shrinkage_conf_post_review.pdf (308.54 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02485823 , version 1 (20-02-2020)


  • HAL Id : hal-02485823 , version 1


Arnaud Breloy, Esa Ollila, Frédéric Pascal. Spectral Shrinkage of Tyler's M -Estimator of Covariance Matrix. IEEE CAMSAP 2019 - IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Dec 2019, Guadeloupe, West Indies, France. ⟨hal-02485823⟩
185 View
219 Download


Gmail Facebook Twitter LinkedIn More