The nonparametric bootstrap and spectral analysis in moderate and highdimension
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Proceedings of Machine Learning Research, PMLR 89:21152124, 2019.
Abstract
We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an n x p data matrix X. We focus on the modern framework where p/n is not close to 0 but remains bounded as n and p tend to infinity. Through a mix of numerical and theoretical considerations, we show that the nonparametric bootstrap is not in general a reliable inferential tool in the setting we consider. However, in the case where the population covariance matrix is wellapproximated by a finite rank matrix, the nonparametric bootstrap performs as it does in finite dimension.
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