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August 2017 New Berry–Esseen bounds for functionals of binomial point processes
Raphaël Lachièze-Rey, Giovanni Peccati
Ann. Appl. Probab. 27(4): 1992-2031 (August 2017). DOI: 10.1214/16-AAP1218

Abstract

We obtain explicit Berry–Esseen bounds in the Kolmogorov distance for the normal approximation of nonlinear 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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Raphaël Lachièze-Rey. Giovanni Peccati. "New Berry–Esseen bounds for functionals of binomial point processes." Ann. Appl. Probab. 27 (4) 1992 - 2031, August 2017. https://doi.org/10.1214/16-AAP1218

Information

Received: 1 May 2015; Revised: 1 January 2016; Published: August 2017
First available in Project Euclid: 30 August 2017

zbMATH: 1374.60023
MathSciNet: MR3693518
Digital Object Identifier: 10.1214/16-AAP1218

Subjects:
Primary: 60F05, 60K35
Secondary: 60D05

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 4 • August 2017
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