Volume 23, 2019
|Page(s)||662 - 671|
|Published online||26 September 2019|
Wald Statistics in high-dimensional PCA★
Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge,
** Corresponding author: email@example.com
Accepted: 10 January 2019
In this study, we consider PCA for Gaussian observations X1, …, Xn with covariance Σ = ∑iλiPi 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 Pr. Using higher order pertubation theory we are able to show that our Theorem remains valid even when .
Mathematics Subject Classification: 62H25 / 62G20 / 62F25
Key words: PCA / spectral projectors / central limit theorem / confidence sets / goodness of fit tests
© EDP Sciences, SMAI 2019
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