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Abstract:
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In many multivariate testing problems, it is necessary to approximate the distribution of certain functions of the eigenvalues of sample covariance matrices (i.e. spectral statistics). Although bootstrap methods are an 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 consider a special class of spectral statistics, and show how a modified version of the bootstrap can provide consistent in-law approximations in the high-dimensional setting.
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