Decompounding: An estimation problem for Poisson random sums

Boris Buchmann; Rudolf Grübel

doi:10.1214/aos/1059655905

Decompounding: An estimation problem for Poisson random sums

Boris Buchmann^*, Rudolf Grübel

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

48 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1054-1074
Number of pages	21
Journal	Annals of Statistics
Volume	31
Issue number	4
DOIs	https://doi.org/10.1214/aos/1059655905
Publication status	Published - Aug 2003
Externally published	Yes

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title = "Decompounding: An estimation problem for Poisson random sums",

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.",

keywords = "Asymptotic normality, Compound distributions, Delta method, Plug-in principle, Queues with bulk arrival, Risk theory",

author = "Boris Buchmann and Rudolf Gr{\"u}bel",

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AU - Grübel, Rudolf

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AB - 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.

KW - Asymptotic normality

KW - Compound distributions

KW - Delta method

KW - Plug-in principle

KW - Queues with bulk arrival

KW - Risk theory

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DO - 10.1214/aos/1059655905

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JO - Annals of Statistics

JF - Annals of Statistics

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Decompounding: An estimation problem for Poisson random sums

Abstract

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