Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory

By Shira Kritchman, Boaz Nadler. IEEE Transactions on Signal Processing, 2009

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Asymptotic power of sphericity tests for high-dimensional data (2013, methodology): “This asymptotic impossibility is also pointed out and discussed in several other recent studies, including Patterson, Price and Reich (2006), Hoyle (2008), Nadler (2008), Kritchman and Nadler (2009) and Perry and Wolfe (2010).”
The Optimal Hard Threshold for Singular Values is $4/\sqrt {3}$ (2014, methodology): “In the closely related Spiked Covariance Model, there are existing methods for estimation of an unknown noise level; see for example [32] and references therein.”
Fluctuations of the Extreme Eigenvalues of Finite Rank Deformations of Random Matrices (2010, background): “This phenomenon was made precise in [9], where a sharp phase transition, known as the BBP transition [34, 27, 38, 29], was exhibited for finite rank perturbations of a complex Gaussian Wishart matrix.”