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- W1975183660 abstract "We consider centered compound Poisson processes with finite variance, discretely observed over $[0,T]$ and let the sampling rate $Delta=Delta_{T}rightarrowinfty$ as $Trightarrowinfty$. 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 for $Delta_{T}$ and we 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 $Delta_{T}$ 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." @default.
- W1975183660 created "2016-06-24" @default.
- W1975183660 creator A5003821012 @default.
- W1975183660 date "2014-01-01" @default.
- W1975183660 modified "2023-09-27" @default.
- W1975183660 title "When is it no longer possible to estimate a compound Poisson process?" @default.
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- W1975183660 doi "https://doi.org/10.1214/14-ejs885" @default.
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