Estimation of the Jump Size Density in a Mixed Compound Poisson Process

Abstract : In this paper, we consider a mixed compound Poisson process, i.e. a random sum of 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. First, 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 nonparametric 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. February 25, 2015
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Scandinavian Journal of Statistics, Wiley, 2015, 42 (4), pp.1023-1044. <10.1111/sjos.12149>
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Soumis le : vendredi 13 novembre 2015 - 09:26:33
Dernière modification le : mardi 11 octobre 2016 - 13:28:50

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Fabienne Comte, Céline Duval, V Genon-Catalot, J Kappus. Estimation of the Jump Size Density in a Mixed Compound Poisson Process. Scandinavian Journal of Statistics, Wiley, 2015, 42 (4), pp.1023-1044. <10.1111/sjos.12149>. <hal-01228389>

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