Abstract
This article studies the robust covariance matrix estimation of a data collection with , where is a concentrated vector (e.g., an elliptical random vector), a deterministic signal and a scalar perturbation of possibly large amplitude, under the assumption where both n and p are large. This estimator is defined as the fixed point of a function which we show is contracting for a so-called stable semi-metric. We exploit this semi-metric along with concentration of measure arguments to prove the existence and uniqueness of the robust estimator as well as evaluate its limiting spectral distribution.
Citation
Cosme Louart. Romain Couillet. "A concentration of measure and random matrix approach to large-dimensional robust statistics." Ann. Appl. Probab. 32 (6) 4737 - 4762, December 2022. https://doi.org/10.1214/22-AAP1801
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