Decompounding:: An estimation problem for Poisson random sums

• 成果类型: Article
• 署名作者: Buchmann, B; Grübel, AR
• 署名单位: Technical University of Munich; Leibniz University Hannover
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2003
• 页码: 1054-1074
• 关键词: nonparametric-estimation; renewal theory

摘要

Given a sample from a compound Poisson distribution, we consider estimation of the corresponding rate parameter and base distribution. This has applications in insurance mathematics and queueing theory. We propose a plug-in type estimator that is based on a suitable inversion of the compounding operation. Asymptotic results for this estimator are obtained via a local analysis of the decompounding functional.