Details
| Original language | English |
|---|---|
| Pages (from-to) | 1054-1074 |
| Number of pages | 21 |
| Journal | Annals of Statistics |
| Volume | 31 |
| Issue number | 4 |
| Publication status | Published - Aug 2003 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Annals of Statistics, Vol. 31, No. 4, 08.2003, p. 1054-1074.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Decompounding
T2 - An estimation problem for Poisson random sums
AU - Buchmann, Boris
AU - Grübel, Rudolf
PY - 2003/8
Y1 - 2003/8
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=0141462756&partnerID=8YFLogxK
U2 - 10.1214/aos/1059655905
DO - 10.1214/aos/1059655905
M3 - Article
AN - SCOPUS:0141462756
VL - 31
SP - 1054
EP - 1074
JO - Annals of Statistics
JF - Annals of Statistics
SN - 0090-5364
IS - 4
ER -