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arXiv · 2305.05646

Estimation of large covariance matrices via free deconvolution: computational and statistical aspects

Reda Chhaibi·Fabrice Gamboa·Slim Kammoun·Mauricio Velasco
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Abstract

The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical resolution of this problem. Our approach is based on complex-analytic methods methods to invert $S$-transforms. In particular, one needs a theoretical understanding of the Riemann surfaces where multivalued $S$ transforms live and an efficient computational scheme.

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Reda Chhaibi, Fabrice Gamboa, Slim Kammoun, Mauricio Velasco. 2023-05-09. Estimation of large covariance matrices via free deconvolution: computational and statistical aspects. https://arxiv.org/abs/2305.05646

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