Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/230737
Authors: 
Götze, Friedrich
Naumov, Alexey
Spokoiny, Vladimir
Ulyanov, Vladimir
Year of Publication: 
2018
Series/Report no.: 
IRTG 1792 Discussion Paper No. 2018-026
Abstract: 
We derive tight non-asymptotic bounds for the Kolmogorov distance between the probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimension-free and depend on the nuclear (Schatten-one) norm of the difference between the covariance operators of the elements and on the norm of the mean shift. The obtained bounds significantly improve the bound based on Pinsker's inequality via the Kullback-Leibler divergence. We also establish an anti-concentration bound for a squared norm of a non-centered Gaussian element in Hilbert space. The paper presents a number of examples motivating our results and applications of the obtained bounds to statistical inference and to high-dimensional CLT.
Subjects: 
Gaussian comparison
Gaussian anti-concentration inequalities
effective rank
dimension free bounds
Schatten norm
high-dimensional inference
JEL: 
C00
Document Type: 
Working Paper

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