The non-parametric bootstrap and spectral analysis in moderate and high-dimension

@InProceedings{pmlr-v89-karoui19a,
  title = 	 {The non-parametric bootstrap and spectral analysis in moderate and high-dimension},
  author =       {Karoui, Noureddine El and Purdom, Elizabeth},
  booktitle = 	 {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
  pages = 	 {2115--2124},
  year = 	 {2019},
  editor = 	 {Chaudhuri, Kamalika and Sugiyama, Masashi},
  volume = 	 {89},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {16--18 Apr},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v89/karoui19a/karoui19a.pdf},
  url = 	 {https://proceedings.mlr.press/v89/karoui19a.html},
  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 non-parametric bootstrap is not in general a reliable inferential tool in the setting we consider. However, in the case where the population covariance matrix is well-approximated by a finite rank matrix, the non-parametric bootstrap performs as it does in finite dimension.}
}