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2022

A short proof of Ledoit-P\'ech\'e's RIE formula for covariance matrices

Benaych-Georges, Florent

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This is a short proof of Ledoit-P\'ech\'e's RIE formula for covariance matrices.

The proof is based on the Stein formula, which gives a very simple way to derive the result.
One of the advantages of this approach is that it shows that the only really needed hypothesis, for the machinery to work, is that the mean of the eigenvalues of the true covariance matrix and the largest of them have the same order.

A short proof of Ledoit-P\'ech\'e's RIE formula for covariance matrices · Around

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Anderson, G., Guionnet, A., Zeitouni, O. An Introduction to Random Matrices . Cambridge Studies in Advanced Mathematics, 118 (2009)
2009
Earlier work this paper cites.
Ledoit, O., Péché, S. Eigenvectors of some large sample covariance matrix ensembles Probability Theory and Related Fields, 2011, 151.1, 233–264
2011
Earlier work this paper cites.

Similar

Benaych-Georges, F., Couillet, R. Spectral analysis of the Gram matrix of mixture models , ESAIM Probab. Statist., Vol. 20 (2016), 217–237
2016
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Benaych-Georges, F., Knowles, A. Local semicircle law for Wigner matrices. Advanced topics in random matrices , 1–90, Panor. Synthèses, 53, Soc. Math. France, Paris, 2017
2017
Cited alongside, same era.

Then

Bun, J., Bouchaud, J.-P., Potters, M. Cleaning large correlation matrices: Tools from Random Matrix Theory , Physics Reports Volume 666, Review article, 1–109, 2017
2017
Later among the works it cites.
Vershynin, R. High-Dimensional Probability: An Introduction with Applications in Data Science , Cambridge Series in Statistical and Probabilistic Mathematics, 2018
Original
2018
Later among the works it cites.

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