Total variation asymptotics for sums of independent integer random variables

Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21917

Barbour, A D; Cekanavicius, V (2002). Total variation asymptotics for sums of independent integer random variables. The Annals of Probability, 30(2):509-545.

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Abstract

Let $W_n := \sum_{j=1}^n Z_j$ be a sum of independent integer-valued random variables. In this paper, we derive an asymptotic expansion for the probability $\mathbb{P}[W_n \in A]$ of an arbitrary subset $A \in \mathbb{Z}$ . Our approximation improves upon the classical expansions by including an explicit, uniform error estimate, involving only easily computable properties of the distributions of the $Z_j:$ an appropriate number of moments and the total variation distance $d_{\mathrm{TV}}(\mathscr{L}(Z_j), \mathscr{L}(Z_j + 1))$ . The proofs are based on Stein’s method for signed compound Poisson approximation.

Item Type:	Journal Article, refereed, original work
Communities & Collections:	07 Faculty of Science > Institute of Mathematics
DDC:	510 Mathematics
Uncontrolled Keywords:	compound Poisson; Stein's method; total variation distance; Kolmogorov's problem
Language:	English
Date:	2002
Deposited On:	07 Apr 2010 12:12
Last Modified:	23 Nov 2012 15:06
Publisher:	Institute of Mathematical Statistics
ISSN:	0091-1798
Publisher DOI:	10.1214/aop/1023481001

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