M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol.55, 1964.

L. Birgé and P. Massart, Minimum Contrast Estimators on Sieves: Exponential Bounds and Rates of Convergence, Bernoulli, vol.4, issue.3, pp.329-375, 1998.
DOI : 10.2307/3318720

B. Bongioanni and J. L. Torrea, What is a Sobolev space for the Laguerre function systems?, Studia Mathematica, vol.192, issue.2, pp.147-172, 2009.
DOI : 10.4064/sm192-2-4

F. Comte, C. Cuenod, M. Pensky, and Y. Rozenholc, Laplace deconvolution on the basis of time domain data and its application to dynamic contrast-enhanced imaging, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.13, issue.158, 2013.
DOI : 10.1111/rssb.12159

F. Comte, C. Duval, and V. Genon-catalot, Nonparametric density estimation in compound Poisson processes using convolution power estimators, Metrika, vol.153, issue.1, pp.163-183, 2014.
DOI : 10.1007/s00184-013-0475-3

F. Comte and V. Genon-catalot, Convolution power kernels for density estimation, Journal of Statistical Planning and Inference, vol.142, issue.7, pp.1698-1715, 2012.
DOI : 10.1016/j.jspi.2012.02.038
URL : https://hal.archives-ouvertes.fr/hal-00681309

L. C. Fabio, G. A. Paula, and M. De-castro, A Poisson mixed model with nonnormal random effect distribution, Computational Statistics & Data Analysis, vol.56, issue.6, pp.1499-1510, 2012.
DOI : 10.1016/j.csda.2011.12.002

J. Fan, On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems, The Annals of Statistics, vol.19, issue.3, pp.1257-1272, 1991.
DOI : 10.1214/aos/1176348248

J. Grandell, Mixed Poisson processes, Monographs on Statistics and Applied Probability, 1997.
DOI : 10.1007/978-1-4899-3117-7

P. Hall and C. C. Heyde, Martingale limit theory and its applications, 1980.

N. W. Hengartner, Adaptive demixing in Poisson mixture models, The Annals of Statistics, vol.25, issue.3, pp.917-928, 1997.
DOI : 10.1214/aos/1069362730

A. F. Karr, Combined nonparametric inference and state estimation for mixed poisson processes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.8, issue.1, pp.81-96, 1984.
DOI : 10.1007/BF00532797

T. Klein and E. Rio, Concentration around the mean for maxima of empirical processes, The Annals of Probability, vol.33, issue.3, pp.1060-1077, 2005.
DOI : 10.1214/009117905000000044

W. Loh and C. Zhang, Global properties of kernel estimators for mixing densities in discrete exponential family models, Statist. Sinica, vol.6, pp.561-578, 1996.

W. Loh and C. Zhang, Estimating Mixing Densities in Exponential Family Models for Discrete Variables, Scandinavian Journal of Statistics, vol.24, issue.1, pp.15-32, 1997.
DOI : 10.1111/1467-9469.t01-1-00046

P. Massart, Concentration inequalities and model selection. Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour Non-life insurance mathematics. An introduction with the Poisson process, Lecture Notes in Mathematics, vol.17, 1896.

J. Shen, Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions, SIAM Journal on Numerical Analysis, vol.38, issue.4, pp.1113-1133, 2000.
DOI : 10.1137/S0036142999362936

L. Simar, Maximum Likelihood Estimation of a Compound Poisson Process, The Annals of Statistics, vol.4, issue.6, pp.1200-1209, 1976.
DOI : 10.1214/aos/1176343651

A. B. Tsybakov, Introduction to nonparametric estimation. Revised and extended from the 2004 French original. Translated by Vladimir Zaiats, 2009.

C. Zhang, On Estimating Mixing Densities in Discrete Exponential Family Models, The Annals of Statistics, vol.23, issue.3, pp.929-945, 1995.
DOI : 10.1214/aos/1176324629