Decompounding: an estimation problem for Poisson random sums

Buchmann, Boris; Grübel, Rudolf

Ann. Statist., Tome 31 (2003) no. 1, p. 1054-1074 / Harvested from Project Euclid

Résumé

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.

Publié le : 2003-08-14
Classification: Risk theory, queues with bulk arrival, compound distributions, plug-in principle, asymptotic normality, delta method, 62G05, 62G20, 62P05

@article{1059655905,
     author = {Buchmann, Boris and Gr\"ubel, Rudolf},
     title = {Decompounding: an estimation problem for Poisson random sums},
     journal = {Ann. Statist.},
     volume = {31},
     number = {1},
     year = {2003},
     pages = { 1054-1074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1059655905}
}

Buchmann, Boris; Grübel, Rudolf. Decompounding: an estimation problem for Poisson random sums. Ann. Statist., Tome 31 (2003) no. 1, pp.  1054-1074. http://gdmltest.u-ga.fr/item/1059655905/