Local Asymptotic Normality of the spectrum of high-dimensional spiked F-ratios
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Abstract
We consider two types of spiked multivariate F distributions: a scaled
distribution with the scale matrix equal to a rank-one perturbation of the
identity, and a distribution with trivial scale, but rank-one non-centrality.
The norm of the rank-one matrix (spike) parameterizes the joint distribution of
the eigenvalues of the corresponding F matrix. We show that, for a spike
located above a phase transition threshold, the asymptotic behavior of the log
ratio of the joint density of the eigenvalues of the F matrix to their joint
density under a local deviation from this value depends only on the largest
eigenvalue