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

Noureddine El Karoui, Elizabeth Purdom
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:2115-2124, 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 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.

Cite this Paper

BibTeX
@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.} }
Endnote
%0 Conference Paper %T The non-parametric bootstrap and spectral analysis in moderate and high-dimension %A Noureddine El Karoui %A Elizabeth Purdom %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-karoui19a %I PMLR %P 2115--2124 %U https://proceedings.mlr.press/v89/karoui19a.html %V 89 %X 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.
APA
Karoui, N.E. & Purdom, E.. (2019). The non-parametric bootstrap and spectral analysis in moderate and high-dimension. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:2115-2124 Available from https://proceedings.mlr.press/v89/karoui19a.html.

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