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The purpose of this note is to provide a detailed proof of Nazarov's inequality stated in Lemma A.1 in Chernozhukov, Chetverikov, and Kato (2017, Annals of Probability).
Nazarov, F. (2003). On the maximal perimeter of a convex set in ℝ n \mathbb{R}^{n} with respect to a Gaussian measure. In: Geometric Aspects of Functional Analysis (2001-2002)
2002
Earlier work this paper cites.
Klivans, A.R., O’Donnel, R. and Servedio, R. (2008). Learning geometric concepts via Gaussian surface area. In: In the Proceedings of the 49th Foundations of Computer Science (FOCS)
2008
Cited alongside, same era.
Chernozhukov, V., Chetverikov, D., and Kato, K. (2017). Central limit theorems and bootstrap in high dimensions. Ann. Probab
2017
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