Exponential inequality for chaos based on sampling without replacement
P Hodara (INRA Jouy en Josas), Patricia Reynaud-Bouret (JAD)
TL;DR
This paper establishes an exponential concentration inequality for specific U-statistics of order 2, known as chaos, in a sampling without replacement setting, advancing understanding of their probabilistic behavior.
Contribution
It introduces a new exponential inequality for chaos functionals derived from sampling without replacement, a setting less explored in existing literature.
Findings
Proves an exponential concentration inequality for U-statistics of order 2
Provides theoretical bounds for chaos functionals in sampling without replacement
Enhances probabilistic analysis tools for dependent sampling scenarios
Abstract
We are interested in the behavior of particular functionals, in a framework where the only source of randomness is a sampling without replacement. More precisely the aim of this short note is to prove an exponential concentration inequality for special U-statistics of order 2, that can be seen as chaos.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Random Matrices and Applications · Point processes and geometric inequalities