Large ball probabilities, Gaussian comparison and anti-concentration

Götze F, Naumov A, Spokoiny V, Ulyanov V (2019)
Bernoulli 25(4A): 2538-2563.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Autor/in
Götze, FriedrichUniBi; Naumov, Alexey; Spokoiny, Vladimir; Ulyanov, Vladimir
Abstract / Bemerkung
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.
Stichworte
dimension free bounds; Gaussian anti-concentration inequalities; Gaussian comparison; high-dimensional CLT; high-dimensional inference; Schatten norm
Erscheinungsjahr
2019
Zeitschriftentitel
Bernoulli
Band
25
Ausgabe
4A
Seite(n)
2538-2563
ISSN
1350-7265
eISSN
1573-9759
Page URI
https://pub.uni-bielefeld.de/record/2937723

Zitieren

Götze F, Naumov A, Spokoiny V, Ulyanov V. Large ball probabilities, Gaussian comparison and anti-concentration. Bernoulli. 2019;25(4A):2538-2563.
Götze, F., Naumov, A., Spokoiny, V., & Ulyanov, V. (2019). Large ball probabilities, Gaussian comparison and anti-concentration. Bernoulli, 25(4A), 2538-2563. doi:10.3150/18-BEJ1062
Götze, F., Naumov, A., Spokoiny, V., and Ulyanov, V. (2019). Large ball probabilities, Gaussian comparison and anti-concentration. Bernoulli 25, 2538-2563.
Götze, F., et al., 2019. Large ball probabilities, Gaussian comparison and anti-concentration. Bernoulli, 25(4A), p 2538-2563.
F. Götze, et al., “Large ball probabilities, Gaussian comparison and anti-concentration”, Bernoulli, vol. 25, 2019, pp. 2538-2563.
Götze, F., Naumov, A., Spokoiny, V., Ulyanov, V.: Large ball probabilities, Gaussian comparison and anti-concentration. Bernoulli. 25, 2538-2563 (2019).
Götze, Friedrich, Naumov, Alexey, Spokoiny, Vladimir, and Ulyanov, Vladimir. “Large ball probabilities, Gaussian comparison and anti-concentration”. Bernoulli 25.4A (2019): 2538-2563.