Uniform concentration bounds for frequencies of rare events

Stéphane Lhaut; Anne Sabourin; Johan Segers

doi:10.1016/j.spl.2022.109610

Uniform concentration bounds for frequencies of rare events

Stéphane Lhaut
, Anne Sabourin
, Johan Segers

University of Louvain
Institut Polytechnique de Paris

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Article number	109610
Journal	Statistics and Probability Letters
Volume	189
DOIs	https://doi.org/10.1016/j.spl.2022.109610
Publication status	Published - 1 Oct 2022
Externally published	Yes

Keywords

Concentration inequalities
Empirical process
Non-parametric
Rare events
VC theory

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10.1016/j.spl.2022.109610

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title = "Uniform concentration bounds for frequencies of rare events",

abstract = "New Vapnik{\textendash}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.",

keywords = "Concentration inequalities, Empirical process, Non-parametric, Rare events, VC theory",

author = "St{\'e}phane Lhaut and Anne Sabourin and Johan Segers",

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year = "2022",

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doi = "10.1016/j.spl.2022.109610",

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T1 - Uniform concentration bounds for frequencies of rare events

AU - Lhaut, Stéphane

AU - Sabourin, Anne

AU - Segers, Johan

PY - 2022/10/1

Y1 - 2022/10/1

N2 - 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.

AB - 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.

KW - Concentration inequalities

KW - Empirical process

KW - Non-parametric

KW - Rare events

KW - VC theory

UR - https://www.scopus.com/pages/publications/85134370576

U2 - 10.1016/j.spl.2022.109610

DO - 10.1016/j.spl.2022.109610

M3 - Article

AN - SCOPUS:85134370576

SN - 0167-7152

VL - 189

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 109610

ER -

Uniform concentration bounds for frequencies of rare events

Abstract

Keywords

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