In this study, we consider PCA for Gaussian observations X1, …, X$$ with covariance Σ = ∑$$λ$$P$$ in the ’effective rank’ setting with model complexity governed by r(Σ) ≔ tr(Σ)∕∥Σ∥. We prove a Berry-Essen type bound for a Wald Statistic of the spectral projector . This can be used to construct non-asymptotic goodness of fit tests and confidence ellipsoids for spectral projectors P$$. Using higher order pertubation theory we are able to show that our Theorem remains valid even when .
Accepté le :
DOI : 10.1051/ps/2019002
Keywords: PCA, spectral projectors, central limit theorem, confidence sets, goodness of fit tests
Löffler, Matthias 1
@article{PS_2019__23__662_0,
author = {L\"offler, Matthias},
title = {Wald {Statistics} in high-dimensional {PCA}},
journal = {ESAIM: Probability and Statistics},
pages = {662--671},
year = {2019},
publisher = {EDP Sciences},
volume = {23},
doi = {10.1051/ps/2019002},
mrnumber = {4011571},
zbl = {1507.62260},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2019002/}
}
Löffler, Matthias. Wald Statistics in high-dimensional PCA. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 662-671. doi: 10.1051/ps/2019002
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