Metrika

, Volume 77, Issue 1, pp 163–183 | Cite as

Nonparametric density estimation in compound Poisson processes using convolution power estimators

  • Fabienne Comte
  • Céline Duval
  • Valentine Genon-Catalot
Article

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.

Keywords

Convolution Compound Poisson process Inverse problem Nonparametric estimation Parameter estimation 

Mathematics Subject Classification (2000)

62G07 60G51 62F12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fabienne Comte
    • 1
  • Céline Duval
    • 1
  • Valentine Genon-Catalot
    • 1
  1. 1.MAP5, UMR CNRS 8145Université Paris DescartesSorbonne Paris CitéFrance

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