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Uniform concentration bounds for frequencies of rare events

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Lhaut, Stéphane [UCL] Sabourin, Anne Segers, Johan [UCL]

New Vapnik–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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2022
Language Anglais
Journal information "Statistics & Probability Letters" - Vol. 189, p. 109610 (2022)
Peer reviewed yes
Publisher Elsevier BV * North-Holland (Amsterdam)
issn 0167-7152
Publication status Publié
Affiliation UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords VC theory ; Concentration Inequalities ; Rare Events ; Empirical Process ; Non-parametric
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Bibliographic reference Lhaut, Stéphane ; Sabourin, Anne ; Segers, Johan. Uniform concentration bounds for frequencies of rare events. In: Statistics & Probability Letters, Vol. 189, p. 109610 (2022)
Permanent URL http://hdl.handle.net/2078.1/263682