The GHOST framework gives near-optimal conditions for universal Gaussian CLTs on linear spectral statistics of sample covariance matrices, with explicit mean-covariance corrections from a bilinear fourth-order kernel and applications to corrected sphericity tests.
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Schott's statistic has an α-free asymptotic for α>3 (relaxed p/n) and a new α-dependent normal limit for α<3, plus a consistent variance estimator usable for all α>0 with unknown locations.
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The Geometry of Spectral Fluctuations: On Near-Optimal Conditions for Universal Gaussian CLTs, with Statistical Applications
The GHOST framework gives near-optimal conditions for universal Gaussian CLTs on linear spectral statistics of sample covariance matrices, with explicit mean-covariance corrections from a bilinear fourth-order kernel and applications to corrected sphericity tests.
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Phase transition of Schott's statistic for high-dimensional heavy-tailed data
Schott's statistic has an α-free asymptotic for α>3 (relaxed p/n) and a new α-dependent normal limit for α<3, plus a consistent variance estimator usable for all α>0 with unknown locations.