Nonparametric density estimation in compound Poisson processes using convolution power estimators

Fabienne Comte (), Céline Duval () and Valentine Genon-Catalot ()

Metrika: International Journal for Theoretical and Applied Statistics, 2014, vol. 77, issue 1, 163-183

Abstract: Consider a compound Poisson process which is discretely observed with sampling interval $$\Delta $$ Δ until exactly $$n$$ n nonzero increments are obtained. The jump density and the intensity of the Poisson process are unknown. In this paper, we build and study parametric estimators of appropriate functions of the intensity, and an adaptive nonparametric estimator of the jump size density. The latter estimation method relies on nonparametric estimators of $$m$$ m th convolution powers density. The $$L^2$$ L 2 -risk of the adaptive estimator achieves the optimal rate in the minimax sense over Sobolev balls. Numerical simulation results on various jump densities enlight the good performances of the proposed estimator. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Convolution; Compound Poisson process; Inverse problem; Nonparametric estimation; Parameter estimation; 62G07; 60G51; 62F12 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:77:y:2014:i:1:p:163-183

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DOI: 10.1007/s00184-013-0475-3

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