A conditional Berry-Esseen inequality
Thierry Klein (IMT), A Lagnoux (IMT), P Petit (IMT)
TL;DR
This paper extends the central limit theorem by establishing a Berry-Esseen inequality for sums of i.i.d. random variables conditioned on another sum of i.i.d. integer-valued variables, providing quantitative bounds.
Contribution
It introduces a new Berry-Esseen inequality for conditioned sums, expanding the theoretical understanding of limit theorems under conditioning.
Findings
Established a Berry-Esseen inequality for conditioned sums
Provided bounds on the rate of convergence in the conditioned CLT
Extended Janson's central limit theorem to include Berry-Esseen bounds
Abstract
As an extension of a central limit theorem established by Svante Janson, we prove a Berry-Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables.
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\authornames
Thierry Klein, Agnès Lagnoux, Pierre Petit