Uniform concentration bounds for frequencies of rare events

Published 12 Oct 2021 in math.ST, math.PR, and stat.TH | (2110.05826v2)

Abstract: New Vapnik and Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on the maximal deviation over classes of Borel sets within a low probability region. The constants are explicit, enabling numerical comparisons.

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