Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/230737 
Erscheinungsjahr: 
2018
Schriftenreihe/Nr.: 
IRTG 1792 Discussion Paper No. 2018-026
Verlag: 
Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series", Berlin
Zusammenfassung: 
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.
Schlagwörter: 
Gaussian comparison
Gaussian anti-concentration inequalities
effective rank
dimension free bounds
Schatten norm
high-dimensional inference
JEL: 
C00
Dokumentart: 
Working Paper

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