Uniform concentration bounds for frequencies of rare events

(2) T\'el\'ecom Paris); Anne Sabourin (2); Johan Segers (1) ((1) Universit\'e Catholique de Louvain; St\'ephane Lhaut (1)

Uniform concentration bounds for frequencies of rare events

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arxiv 2110.05826 v2 pith:CQZOLQQK submitted 2021-10-12 math.ST math.PRstat.TH

Stéphane Lhaut (1) , Anne Sabourin (2) , Johan Segers (1) ((1) Université Catholique de Louvain , (2) Télécom Paris) This is my paper · ORCID

classification math.STmath.PRstat.TH

keywords concentrationborelboundschervonenkisclassescomparisonsconstantsderived

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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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