Refined total variation bounds in the multivariate and compound Poisson approximation
Probability
2017-03-08 v2
Abstract
We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better structure than those from the literature. A numerical example illustrates the usefulness of the bounds, and an application in the Poisson process approximation is given. The proofs use arguments from Kerstan (Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 (1964) 173-179) and Roos (J. Multivariate Anal. 69 (1999) 120-134) in combination with new smoothness inequalities, which could be of independent interest.
Cite
@article{arxiv.1509.04167,
title = {Refined total variation bounds in the multivariate and compound Poisson approximation},
author = {Bero Roos},
journal= {arXiv preprint arXiv:1509.04167},
year = {2017}
}
Comments
Revised and enlarged. 24 pages