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August 2003 Decompounding: an estimation problem for Poisson random sums
Boris Buchmann, Rudolf Grübel
Ann. Statist. 31(4): 1054-1074 (August 2003). DOI: 10.1214/aos/1059655905

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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Boris Buchmann. Rudolf Grübel. "Decompounding: an estimation problem for Poisson random sums." Ann. Statist. 31 (4) 1054 - 1074, August 2003. https://doi.org/10.1214/aos/1059655905

Information

Published: August 2003
First available in Project Euclid: 31 July 2003

zbMATH: 1105.62309
MathSciNet: MR2001642
Digital Object Identifier: 10.1214/aos/1059655905

Subjects:
Primary: 62G05
Secondary: 62G20 , 62P05

Keywords: asymptotic normality , compound distributions , Delta method , plug-in principle , queues with bulk arrival , Risk theory

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 4 • August 2003
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