Abstract
Let ℕ n and\(\mathbb{B}_\mu \) be an empirical process and a generalized Brownian bridge, respectively, indexed by a class ℱ of real measurable functions. From the central limit theorem for empirical processes it follows that
for allr≥0. In this paper, assuming the class ℱ to be countably determined, under certain conditions we obtain an estimate
for some constantC. Vapnik-Červonenkis class and the indicators of lower left orthants provide examples of classes ℱ considered here.
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Norvaiša, R., Paulauskas, V. Rate of convergence in the central limit theorem for empirical processes. J Theor Probab 4, 511–534 (1991). https://doi.org/10.1007/BF01210322
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DOI: https://doi.org/10.1007/BF01210322