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Abstract:
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In many multivariate testing problems, it is necessary to know the distribution of certain functions of the eigenvalues of sample covariance matrices (i.e. spectral statistics). Although bootstrap methods are a well established approach to approximating the laws of spectral statistics in low-dimensional problems, their extension to the high-dimensional setting is relatively unexplored. In our work, we show how a decay constraint in the population spectrum can lead to consistent-in-law approximations of spectral statistics by way of the bootstrap, even when the problem is high-dimensional.
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