A. Barron, L. Birgé, and P. Massart, Risk bounds for model selection via penalization, Probability Theory and Related Fields, vol.113, issue.3, pp.301-413, 1999.
DOI : 10.1007/s004400050210

J. Baudry, C. Maugis, and B. Michel, Slope heuristics: overview and implementation, Statistics and Computing, vol.6, issue.2, pp.455-470, 2012.
DOI : 10.1214/aos/1176344136

URL : https://hal.archives-ouvertes.fr/hal-00461639

M. Bec and C. Lacour, Adaptive pointwise estimation for pure jump L??vy processes, Statistical Inference for Stochastic Processes, pp.229-256, 2015.
DOI : 10.1080/0094965021000015477

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. Buchmann and R. Grübel, Decompounding: an estimation problem for Poisson random sums, Ann. Statist, vol.314, pp.1054-1074, 2003.

C. Butucea and A. B. Tsybakov, Sharp optimality in density deconvolution with dominating bias. I ", In: Teor. Veroyatn. Primen, vol.521, pp.111-128, 2007.

C. Butucea and A. B. Tsybakov, Sharp optimality in density deconvolution with dominating bias. II, Teoriya Veroyatnostei i ee Primeneniya, vol.52, issue.2, pp.336-349, 2007.
DOI : 10.4213/tvp175

C. Butucea, Deconvolution of supersmooth densities with smooth noise, Canadian Journal of Statistics, vol.330, issue.2, pp.181-192, 2004.
DOI : 10.1214/lnms/1215090078

URL : https://hal.archives-ouvertes.fr/hal-00103058

R. J. Carroll and P. Hall, Optimal rates of convergence for deconvolving a density, Journal of the American Statistical Association, vol.83404, pp.1184-1186, 1988.

A. J. Coca, Efficient nonparametric inference for discretely observed compound Poisson processes, Probability Theory and Related Fields, pp.1-49, 2017.
DOI : 10.1090/S0002-9939-1985-0806089-1

F. Comte, Y. Rozenholc, and M. Taupin, Finite sample penalization in adaptive density deconvolution, Journal of Statistical Computation and Simulation, vol.1, issue.11, pp.11-12, 2007.
DOI : 10.2307/3316026

URL : https://hal.archives-ouvertes.fr/hal-00016503

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 : 10.1016/j.jeconom.2009.04.007

F. Comte and V. Genon-catalot, Nonparametric adaptive estimation for pure jump L??vy processes, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.3, pp.595-617, 2010.
DOI : 10.1214/09-AIHP323

F. Comte and J. Kappus, Density deconvolution from repeated measurements without symmetry assumption on the errors, Journal of Multivariate Analysis, vol.140, pp.31-46, 2015.
DOI : 10.1016/j.jmva.2015.04.004

URL : https://hal.archives-ouvertes.fr/hal-01010409

F. Comte and C. Lacour, Anisotropic adaptive kernel deconvolution, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.49, issue.2, pp.569-609
DOI : 10.1214/11-AIHP470

URL : https://hal.archives-ouvertes.fr/hal-00579608

F. Comte and C. Lacour, Data-driven density estimation in the presence of additive noise with unknown distribution, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.18, issue.4, pp.601-627, 2011.
DOI : 10.1214/aos/1176347627

F. Comte, Y. Rozenholc, and M. Taupin, Finite sample penalization in adaptive density deconvolution, Journal of Statistical Computation and Simulation, vol.1, issue.11, pp.977-1000, 2007.
DOI : 10.2307/3316026

URL : https://hal.archives-ouvertes.fr/hal-00016503

A. Delaigle and I. Gijbels, Practical bandwidth selection in deconvolution kernel density estimation, Computational statistics & data analysis 45, pp.249-267, 2004.
DOI : 10.1016/S0167-9473(02)00329-8

A. Delaigle, P. Hall, and A. Meister, On deconvolution with repeated measurements, The Annals of Statistics, vol.36, issue.2, pp.665-685, 2008.
DOI : 10.1214/009053607000000884

S. Delattre, M. Hoffmann, D. Picard, and T. Vareschi, Blockwise SVD with error in the operator and application to blind deconvolution, Electronic Journal of Statistics, vol.6, issue.0, pp.2274-2308, 2012.
DOI : 10.1214/12-EJS745

URL : https://hal.archives-ouvertes.fr/hal-00779777

D. L. Donoho and I. M. Johnstone, Ideal spatial adaptation by wavelet shrinkage, Biometrika, vol.81, issue.3, pp.425-455, 1994.
DOI : 10.1093/biomet/81.3.425

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, Wavelet shrinkage: asymptopia?, In: Journal of the Royal Statistical Society. Series B (Methodological), pp.301-369, 1995.

C. Duval, Density estimation for compound Poisson processes from discrete data, Stochastic Process, pp.3963-3986, 2013.
DOI : 10.1016/j.spa.2013.06.006

C. Duval, When is it no longer possible to estimate a compound Poisson process?, Electronic Journal of Statistics, vol.8, issue.1, pp.274-301, 2014.
DOI : 10.1214/14-EJS885

URL : https://hal.archives-ouvertes.fr/hal-00877195

C. Duval and J. Kappus, Nonparametric adaptive estimation for grouped data, Journal of Statistical Planning and Inference, vol.182, pp.12-28, 2017.
DOI : 10.1016/j.jspi.2016.10.002

URL : https://hal.archives-ouvertes.fr/hal-01245781

B. Van-es, S. Gugushvili, and P. Spreij, A kernel type nonparametric density estimator for decompounding, Bernoulli, vol.13, issue.3, pp.672-694, 2007.
DOI : 10.3150/07-BEJ6091

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

A. Goldenshluger and O. Lepski, Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality, The Annals of Statistics, vol.39, issue.3, pp.1608-1632, 2011.
DOI : 10.1214/11-AOS883

URL : https://hal.archives-ouvertes.fr/hal-01265258

A. Goldenshluger and O. Lepski, On adaptive minimax density estimation on R?dR?d, Probability Theory and Related Fields, pp.3-4, 2014.

A. Goldenshluger and O. Lepski, Universal pointwise selection rule in multivariate function estimation, Bernoulli, vol.14, issue.4, pp.1150-1190, 2008.
DOI : 10.3150/08-BEJ144

A. Goldenshluger and O. Lepski, General Selection Rule from a Family of Linear Estimators, Theory of Probability & Its Applications 57, pp.209-226, 2013.
DOI : 10.1137/S0040585X97985923

S. Gugushvili, Nonparametric inference for discretely sampled L??vy processes, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.48, issue.1, pp.282-307
DOI : 10.1214/11-AIHP433

S. Gugushvili, F. Van-der-meulen, and P. Spreij, Nonparametric Bayesian inference for multidimensional compound Poisson processes, Modern Stochastics: Theory and Applications, vol.2, issue.1, p.7739, 2014.
DOI : 10.15559/15-VMSTA20

J. Johannes, Deconvolution with unknown error distribution, The Annals of Statistics, vol.37, issue.5A, pp.2301-2323, 2009.
DOI : 10.1214/08-AOS652

J. Johannes and M. Schwarz, Adaptive circular deconvolution by model selection under unknown error distribution, Bernoulli, vol.19, issue.5A, pp.1576-1611, 2013.
DOI : 10.3150/12-BEJ422

J. Kappus, Adaptive nonparametric estimation for L??vy processes observed at low frequency, Stochastic Process, pp.730-758, 2014.
DOI : 10.1016/j.spa.2013.08.010

J. Kappus and G. Mabon, Adaptive density estimation in deconvolution problems with unknown error distribution, Electronic journal of statistics 8, pp.2879-2904, 2014.
DOI : 10.1214/14-EJS976

URL : https://hal.archives-ouvertes.fr/hal-00915982

C. Lacour, P. Massart, and V. Rivoirard, Estimator Selection: a New Method with Applications to Kernel Density Estimation, Sankhya A 79, pp.298-335, 2017.
DOI : 10.1007/978-1-4899-3324-9

URL : https://hal.archives-ouvertes.fr/hal-01346081

O. Lepskii, Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates, Theory of Probability & Its Applications 36, pp.682-697, 1992.
DOI : 10.1137/1136085

O. Lepskii, On a Problem of Adaptive Estimation in Gaussian White Noise, Theory of Probability & Its Applications, vol.35, issue.3, pp.454-466, 1991.
DOI : 10.1137/1135065

M. Lerasle, Optimal model selection in density estimation, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.48, issue.3, pp.884-908
DOI : 10.1214/11-AIHP425

URL : https://hal.archives-ouvertes.fr/hal-00422655

K. Lounici and R. Nickl, Global uniform risk bounds for wavelet deconvolution estimators, The Annals of Statistics, vol.39, issue.1, pp.201-231, 2011.
DOI : 10.1214/10-AOS836

URL : http://doi.org/10.1214/10-aos836

P. Massart, Concentration inequalities and model selection, 2007.

A. Meister, Deconvolution problems in nonparametric statistics, 2009.
DOI : 10.1007/978-3-540-87557-4

A. Meister, Optimal convergence rates for density estimation from grouped data & probability letters 77, Statistics, vol.11, pp.1091-1097, 2007.

M. H. Neumann, On the effect of estimating the error density in nonparametric deconvolution, Journal of Nonparametric Statistics, vol.46, issue.4, pp.307-330, 1997.
DOI : 10.1007/978-1-4899-4493-1

M. H. Neumann and M. Reiß, Nonparametric estimation for L??vy processes from low-frequency observations, Bernoulli, vol.15, issue.1, pp.223-248, 2009.
DOI : 10.3150/08-BEJ148

M. Pensky and B. Vidakovic, Adaptive wavelet estimator for nonparametric density deconvolution, The Annals of Statistics, vol.276, pp.2033-2053, 1999.

G. Rebelles, Structural adaptive deconvolution under $${\mathbb{L}_p}$$ -losses, Mathematical Methods of Statistics, vol.17, issue.1, pp.26-53, 2016.
DOI : 10.1007/s11749-006-0027-5

URL : https://hal.archives-ouvertes.fr/hal-01309246

P. Reynaud-bouret, V. Rivoirard, and C. Tuleau-malot, Adaptive density estimation: A curse of support?, Journal of Statistical Planning and Inference, vol.141, issue.1, pp.115-139, 2011.
DOI : 10.1016/j.jspi.2010.05.017

URL : https://hal.archives-ouvertes.fr/hal-00634421

L. A. Stefanski, Rates of convergence of some estimators in a class of deconvolution problems & Probability Letters 9, Statistics, vol.3, pp.229-235, 1990.

L. A. Stefanski and R. J. Carroll, Deconvolving kernel density estimators, Statistics, vol.48, issue.2, pp.169-184, 1990.
DOI : 10.1109/TIT.1977.1055802