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 vec- tors of independent random variables. Our results are based on the use of Stein’s method and of random difference operators, and gen- eralise 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 decom- positions, for which we provide a new proof and a new representa- tion. Several applications are discussed in detail: in particular, new Berry-Esseen bounds are obtained for set approximations with ran- dom 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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