Wald Statistics in high-dimensional PCA
ESAIM: Probability and Statistics, Tome 23 (2019), pp. 662-671.

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 P ^ r . 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 𝐫(Σ)≫n.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2019002
Classification : 62H25, 62G20, 62F25
Mots-clés : PCA, spectral projectors, central limit theorem, confidence sets, goodness of fit tests
Löffler, Matthias 1

1 
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     journal = {ESAIM: Probability and Statistics},
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     publisher = {EDP-Sciences},
     volume = {23},
     year = {2019},
     doi = {10.1051/ps/2019002},
     mrnumber = {4011571},
     zbl = {1507.62260},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2019002/}
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Löffler, Matthias. Wald Statistics in high-dimensional PCA. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 662-671. doi : 10.1051/ps/2019002. http://www.numdam.org/articles/10.1051/ps/2019002/

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