Kerstan's method for compound Poisson approximation

• 成果类型: Article
• 署名作者: Roos, B
• 署名单位: University of Hamburg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1068646365
• 发表日期: 2003
• 页码: 1754-1771
• 关键词: constants

摘要

We consider the approximation of the distribution of the sum of independent but not necessarily identically distributed random variables by a compound Poisson distribution and also by a finite signed measure of higher accuracy. Using Kerstan's method, some new bounds for the total variation distance are presented. Recently, several authors had difficulties applying Stein's method to the problem given. For instance, Barbour, Chen and Loh used this method in the case of random variables on the nonnegative integers. Under additional assumptions, they obtained some bounds for the total variation distance containing an undesirable log term. In the present paper, we shall show that Kerstan's approach works without such restrictions and yields bounds without log terms.