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Journal Articles Metrika Year : 2014

Nonparametric density estimation in compound Poisson process using convolution power estimators.

Abstract

Consider a compound Poisson process which is discretely observed with sampling interval $\Delta$ until exactly $n$ 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 $m$-th convolution powers density. The $L^2$-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.
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Dates and versions

hal-00780300 , version 1 (23-01-2013)

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Cite

Fabienne Comte, Céline Duval, Valentine Genon-Catalot. Nonparametric density estimation in compound Poisson process using convolution power estimators.. Metrika, 2014, 77 (1), pp.163-183. ⟨10.1007/s00184-013-0475-3⟩. ⟨hal-00780300⟩
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