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Conference Papers Year : 2019

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

Abstract

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.
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Dates and versions

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

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Arnaud Breloy, Esa Ollila, Frédéric Pascal. Spectral Shrinkage of Tyler's M -Estimator of Covariance Matrix. 8th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2019), Dec 2019, Guadeloupe, West Indies, France. ⟨10.1109/camsap45676.2019.9022652⟩. ⟨hal-02485823⟩
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