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Bernoulli

Stein’s method and Poisson process approximation for a class of Wasserstein metrics

Dominic Schuhmacher

Source: Bernoulli Volume 15, Number 2 (2009), 550-568.

Abstract

Based on Stein’s method, we derive upper bounds for Poisson process approximation in the L1-Wasserstein metric d2(p), which is based on a slightly adapted Lp-Wasserstein metric between point measures. For the case p=1, this construction yields the metric d2 introduced in [Barbour and Brown Stochastic Process. Appl. 43 (1992) 9–31], for which Poisson process approximation is well studied in the literature. We demonstrate the usefulness of the extension to general p by showing that d2(p)-bounds control differences between expectations of certain pth order average statistics of point processes. To illustrate the bounds obtained for Poisson process approximation, we consider the structure of 2-runs and the hard core model as concrete examples.

Keywords: Barbour-Brown metric; distributional approximation; L_p-Wasserstein metric; Poisson point process; Stein’s method

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bj/1241444902
Digital Object Identifier: doi:10.3150/08-BEJ161
Mathematical Reviews number (MathSciNet): MR2543874

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