The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 27, Number 4 (2017), 1992-2031.
New Berry–Esseen bounds for functionals of binomial point processes
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.
Ann. Appl. Probab., Volume 27, Number 4 (2017), 1992-2031.
Received: May 2015
Revised: January 2016
First available in Project Euclid: 30 August 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Lachièze-Rey, Raphaël; Peccati, Giovanni. New Berry–Esseen bounds for functionals of binomial point processes. Ann. Appl. Probab. 27 (2017), no. 4, 1992--2031. doi:10.1214/16-AAP1218. https://projecteuclid.org/euclid.aoap/1504080024