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pdf Research Kengo Kato

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Comments on “Gaussian approximation of suprema of empirical processes” (V. Chernozhukov, D. Chetverikov, K. Kato)

2014.9.5./2017.2.18. (1) In the statement of Corollary 2.2, “for k = 2, 3” should be “for k= 2, 3, 4”. This typo happened in the course of the editorial process and is corrected in the full version posted in arXiv.

(2) Except for Corollary 2.2, q = ∞ is excluded (e.g. Theorem 5.1 does not hold with q = ∞). Corollary 2.2 is true, and the constants c, C in the corollary can be independent of q. The proof of Corollary 2.2 is bit misleading, but we apply Theorem 2.1 in the proof with q = 4, and use “higher” q to obtain the moment bounds.

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