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Multivariate Second-Order $p$-Poincar\'e Inequalities
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abstract
In this work, we discuss new bounds for the normal approximation of multivariate Poisson functionals under minimal moment assumptions. Such bounds require one to estimate moments of so-called add-one costs of the functional. Previous works required the estimation of $4^{\text{th}}$ moments, while our result only requires $(2 + \epsilon)$-moments, based on recent improvements introduced by (Trauthwein 2022). As applications, we show quantitative CLTs for two multivariate functionals of the Gilbert, or random geometric, graph. These examples were out of range for previous methods.
Forward citations
Cited by 2 Pith papers
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The Poisson Multiplication Formula
Products of m Poisson multiple integrals are square-integrable exactly when iterated add-one cost expectations lie in L2, and their chaos kernels are explicit partition sums.
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Normal approximation for subgraph counts in age-dependent random connection models
Clique and subtree counts in the age-dependent random connection model are asymptotically normal in the light-tailed regime, with quantitative bounds for cliques.
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