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The Local Ledoit-Peche Law

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arxiv 2302.13708 v1 pith:AFUDU6J2 submitted 2023-02-27 math.ST stat.TH

Van Latimer , Benjamin D. Robinson This is my paper · ORCID
classification math.STstat.TH
keywords convergencecovarianceledoitledoit-pechelossrateshrinkageapplication
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Ledoit and Peche proved convergence of certain functions of a random covariance matrix's resolvent; we refer to this as the Ledoit-Peche law. One important application of their result is shrinkage covariance estimation with respect to so-called Minimum Variance (MV) loss, discussed in the work of Ledoit and Wolf. We provide an essentially optimal rate of convergence and hypothesize it to be the smallest possible rate of excess MV loss within the shrinkage class.

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  1. Spectrally Robust Covariance Shrinkage for Hotelling's $T^2$ in High Dimensions

    math.ST 2025-02 conditional novelty 6.0 of 10

    A variational argument yields an asymptotically power-optimal covariance shrinker for high-dimensional Hotelling's T-squared tests under general covariance spectra.

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