The Non-Parametric Bootstrap and Spectral Analysis in Moderate and High-Dimension
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
Text
El Karoui and Purdom. "The Non-Parametric Bootstrap and Spectral Analysis in Moderate and High-Dimension." Artificial Intelligence and Statistics, 2019.Markdown
[El Karoui and Purdom. "The Non-Parametric Bootstrap and Spectral Analysis in Moderate and High-Dimension." Artificial Intelligence and Statistics, 2019.](https://mlanthology.org/aistats/2019/karoui2019aistats-nonparametric/)BibTeX
@inproceedings{karoui2019aistats-nonparametric,
title = {{The Non-Parametric Bootstrap and Spectral Analysis in Moderate and High-Dimension}},
author = {El Karoui, Noureddine and Purdom, Elizabeth},
booktitle = {Artificial Intelligence and Statistics},
year = {2019},
pages = {2115-2124},
volume = {89},
url = {https://mlanthology.org/aistats/2019/karoui2019aistats-nonparametric/}
}