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Decompounding: an estimation problem for Poisson random sums

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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.

Description

Keywords

Keywords: Asymptotic normality; Compound distributions; Delta method; Plug-in principle; Queues with bulk arrival; Risk theory

Citation

URI

http://hdl.handle.net/1885/99989

Collections

ANU Research Publications

Source

The Annals of Statistics

Type

Journal article

Book Title

Entity type

Access Statement

Open Access

License Rights

DOI

10.1214/aos/1059655905

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