New Berry-Esseen bounds for functionals of binomial point processes

Abstract : We obtain explicit Berry-Esseen bounds in the Kolmogorov dis- tance for the normal approximation of non-linear functionals of vectors of independent random variables. Our results are based on the use of Stein’s method and of random difference operators, and generalise the bounds obtained by Chatterjee (2008), concerning normal approximations in the Wasserstein distance. In order to obtain lower bounds for variances, we also revisit the classical Hoeffding decompositions, for which we provide a new proof and a new representation. Several applications are discussed in detail: in particular, new Berry-Esseen bounds are obtained for set approximations with random tessellations, as well as for functionals of coverage processes.
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The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2017, 27 (4), pp.1992-2031. 〈https://projecteuclid.org/euclid.aoap/1504080024〉
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  • HAL Id : hal-01155629, version 2
  • ARXIV : 1505.04640

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Raphaël Lachièze-Rey, Giovanni Peccati. New Berry-Esseen bounds for functionals of binomial point processes. The Annals of Applied Probability : an official journal of the institute of mathematical statistics, The Institute of Mathematical Statistics, 2017, 27 (4), pp.1992-2031. 〈https://projecteuclid.org/euclid.aoap/1504080024〉. 〈hal-01155629v2〉

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