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http://dx.doi.org/10.25673/42131
Titel: | Decompounding discrete distributions : a nonparametric Bayesian approach |
Autor(en): | Gugushvili, Shota Mariucci, Ester Meulen, Frank |
Erscheinungsdatum: | 2020 |
Art: | Artikel |
Sprache: | Englisch |
URN: | urn:nbn:de:gbv:ma9:1-1981185920-440853 |
Schlagwörter: | Poisson process Nonparametric Bayesian approach Markov chain Monte Carlo scheme |
Zusammenfassung: | Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a nonparametric Bayesian approach to estimate the intensity of the underlying Poisson process and the distribution of the jumps. We provide a Markov chain Monte Carlo scheme for obtaining samples from the posterior. We apply our method on both simulated and real data examples, and compare its performance with the frequentist plug-in estimator proposed by Buchmann and Grübel. On a theoretical side, we study the posterior from the frequentist point of view and prove that as the sample size n→∞, it contracts around the “true,” data-generating parameters at rate 1/𝑛⎯⎯√, up to a log𝑛 factor. |
URI: | https://opendata.uni-halle.de//handle/1981185920/44085 http://dx.doi.org/10.25673/42131 |
Open-Access: | Open-Access-Publikation |
Nutzungslizenz: | (CC BY 4.0) Creative Commons Namensnennung 4.0 International |
Sponsor/Geldgeber: | Projekt DEAL 2019 |
Journal Titel: | Scandinavian journal of statistics |
Verlag: | Wiley-Blackwell |
Verlagsort: | Oxford |
Band: | 47 |
Heft: | 2 |
Originalveröffentlichung: | 10.1111/sjos.12413 |
Seitenanfang: | 464 |
Seitenende: | 492 |
Enthalten in den Sammlungen: | Fakultät für Mathematik (OA) |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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Gugushvili et al._Decompounding_2020.pdf | Zweitveröffentlichung | 1.11 MB | Adobe PDF | Öffnen/Anzeigen |