Decompounding: an estimation problem for Poisson random sums
Date
2003
Authors
Buchmann, Boris
Grübel, Rudolf
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Mathematical Statistics
Abstract
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.
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Keywords
Keywords: Asymptotic normality; Compound distributions; Delta method; Plug-in principle; Queues with bulk arrival; Risk theory
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Source
The Annals of Statistics
Type
Journal article
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Open Access
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