Total variation asymptotics for sums of independent integer random variables

• 成果类型: Article
• 署名作者: Barbour, AD; Cekanavicius, V
• 署名单位: University of Zurich; Vilnius University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 509-545
• 关键词: compound poisson approximation; SEQUENCES

摘要

Let W-n := Sigma(j-1)(n) (Zj) be a sum of independent integer-valued random variables. In this paper, we derive an asymptotic expansion for the probability P[W-n is an element of A] of an arbitrary subset A is an element of 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(TV) (X (Zj), L(Z(j) + 1)). The proofs are based on Stein's method for signed compound Poisson approximation.