Estimation of the Jump Size Density in a Mixed Compound Poisson Process |
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| Authors: | Fabienne Comte Celine Duval Valentine Genon‐Catalot Johanna Kappus |
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| Affiliation: | 1. MAP5, UMR CNRS 8145, Université Paris Descartes, Paris, France;2. Institut für Mathematik, Universit?t Rostock, Germany |
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| Abstract: | In this paper, we consider a mixed compound Poisson process, that is, a random sum of independent and identically distributed (i.i.d.) random variables where the number of terms is a Poisson process with random intensity. We study nonparametric estimators of the jump density by specific deconvolution methods. Firstly, assuming that the random intensity has exponential distribution with unknown expectation, we propose two types of estimators based on the observation of an i.i.d. sample. Risks bounds and adaptive procedures are provided. Then, with no assumption on the distribution of the random intensity, we propose two non‐parametric estimators of the jump density based on the joint observation of the number of jumps and the random sum of jumps. Risks bounds are provided, leading to unusual rates for one of the two estimators. The methods are implemented and compared via simulations. |
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| Keywords: | adaptive methods deconvolution mixed compound Poisson process non‐parametric density estimation penalization method |
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