# When is it no longer possible to estimate a compound Poisson process?

Abstract : We consider centered compound Poisson processes with fi nite variance, discretely observed over [0; T] and let the sampling rate $\Delta$ go to infinity as T tends to infinity. From the central limit theorem, the law of each increment converges to a Gaussian variable. Then, it should not be possible to estimate more than one parameter at the limit. First, from the study of a parametric example we identify two regimes and observe how the Fisher information degenerates. Then, we generalize these results to the class of compound Poisson processes. We establish a lower bound showing that consistent estimation is impossible when $\Delta$ grows faster than $\sqrt{T}$. We also prove an asymptotic equivalence result, from which we identify, for instance, regimes where the increments cannot be distinguished from Gaussian variables.
Type de document :
Article dans une revue
Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2014, 8, pp.274-301. 〈10.1214/14-EJS885〉
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https://hal.archives-ouvertes.fr/hal-00877195
Contributeur : Céline Duval <>
Soumis le : lundi 11 août 2014 - 14:03:04
Dernière modification le : jeudi 11 janvier 2018 - 06:19:45
Document(s) archivé(s) le : mercredi 26 novembre 2014 - 22:05:51

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Céline Duval. When is it no longer possible to estimate a compound Poisson process?. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2014, 8, pp.274-301. 〈10.1214/14-EJS885〉. 〈hal-00877195v2〉

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