Uniform concentration bounds for frequencies of rare events

2021/10/12 by Stéphane Lhaut, Lhaut, Stéphane, Anne Sabourin +3 · 2 citations
Computer Science · Mathematics · #62G05 (Secondary) #62G30 (Primary) #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2110.05826

openalex publication_date 2021/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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