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Uniform concentration bounds for frequencies of rare events

Author

Listed:
  • Lhaut, Stéphane

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Sabourin, Anne

    (Institut polytechnique de Paris)

  • Segers, Johan

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

New Vapnik–Chervonkis 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.

Suggested Citation

  • Lhaut, Stéphane & Sabourin, Anne & Segers, Johan, 2021. "Uniform concentration bounds for frequencies of rare events," LIDAM Discussion Papers ISBA 2021034, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2021034
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