A. Banyaga and D. Hurtubise, Lectures on Morse Homology, 2004.
DOI : 10.1007/978-1-4020-2696-6

V. Bentkus, On the dependence of the Berry???Esseen bound on dimension, Journal of Statistical Planning and Inference, vol.113, issue.2, pp.385-402, 2003.
DOI : 10.1016/S0378-3758(02)00094-0

G. Biau, F. Chazal, D. Cohen-steiner, L. Devroye, and C. Rodriguez, A weighted k-nearest neighbor density estimate for geometric inference, Electronic Journal of Statistics, vol.5, issue.0, pp.204-237, 2011.
DOI : 10.1214/11-EJS606

URL : https://hal.archives-ouvertes.fr/inria-00560623

S. Bobkov and M. Ledoux, One-dimensional empirical measures, order statistics and Kantorovich transport distances, 2014.

O. Bobrowski, S. Mukherjee, and J. Taylor, Topological consistency via kernel estimation. arXiv preprint, 2014.
DOI : 10.3150/15-bej744

URL : http://arxiv.org/abs/1407.5272

P. Bubenik, Statistical topological data analysis using persistence landscapes, Journal of Machine Learning Research, vol.16, pp.77-102, 2015.

M. Buchet, F. Chazal, Y. Steve, . Oudot, R. Donald et al., Efficient and robust topological data analysis on metric spaces, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00831729

C. Caillerie, F. Chazal, J. Dedecker, and B. Michel, Deconvolution for the Wasserstein metric and geometric inference, Electronic Journal of Statistics, vol.5, issue.0, pp.1394-1423, 2011.
DOI : 10.1214/11-EJS646

URL : https://hal.archives-ouvertes.fr/inria-00607806

G. Carlsson, Topology and data. Bulletin of the, pp.255-308, 2009.

F. Chazal, D. Cohen-steiner, M. Glisse, L. J. Guibas, and S. Y. Oudot, Proximity of persistence modules and their diagrams, Proceedings of the 25th annual symposium on Computational geometry, SCG '09, pp.237-246, 2009.
DOI : 10.1145/1542362.1542407

URL : https://hal.archives-ouvertes.fr/inria-00292566

F. Chazal, V. De-silva, M. Glisse, and S. Oudot, The structure and stability of persistence modules. arXiv preprint arXiv:1207, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01107617

F. Chazal, D. Cohen-steiner, and Q. Mérigot, Geometric Inference for Probability Measures, Foundations of Computational Mathematics, vol.40, issue.2, pp.733-751, 2011.
DOI : 10.1007/s10208-011-9098-0

URL : https://hal.archives-ouvertes.fr/hal-00772444

F. Chazal, P. Massart, and B. Michel, Rates of convergence for robust geometric inference, Electronic Journal of Statistics, vol.10, issue.2, 2015.
DOI : 10.1214/16-EJS1161

URL : https://hal.archives-ouvertes.fr/hal-01157551

D. Cohen-steiner, H. Edelsbrunner, and J. Harer, Stability of persistence diagrams, SCG, pp.263-271, 2005.

A. Cuevas and A. Rodríguez, On boundary estimation, Advances in Applied Probability, vol.21, issue.02, pp.340-354, 2004.
DOI : 10.1002/(SICI)1099-1476(19990310)22:4<301::AID-MMA42>3.0.CO;2-M

M. Demazure, Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear Problems, 2013.
DOI : 10.1007/978-3-642-57134-3

H. Edelsbrunner and J. Harer, Computational Topology: An Introduction, 2010.
DOI : 10.1090/mbk/069

B. T. Fasy, J. Kim, F. Lecci, and C. Maria, Introduction to the R package TDA. arXiv preprint, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01113028

B. T. Fasy, F. Lecci, A. Rinaldo, L. Wasserman, S. Balakrishnan et al., Confidence sets for persistence diagrams. The Annals of Statistics, pp.2301-2339, 2014.

E. Giné and A. Guillou, Rates of strong uniform consistency for multivariate kernel density estimators, Annales de l'Institut Henri Poincare (B) Probability and Statistics, pp.907-921, 2002.
DOI : 10.1016/S0246-0203(02)01128-7

M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities, 1986.
DOI : 10.1007/978-1-4615-7904-5

L. Guibas, D. Morozov, and Q. Mérigot, Witnessed k-Distance, Discrete & Computational Geometry, vol.40, issue.2, pp.22-45, 2013.
DOI : 10.1007/s00454-012-9465-x

URL : https://hal.archives-ouvertes.fr/hal-00872490

V. Icke and R. Van-de-weygaert, The Galaxy Distribution as a Voronoi Foam, Quarterly Journal of the Royal Astronomical Society, vol.32, pp.85-112, 1991.
DOI : 10.1007/978-3-663-01466-9_8

J. /. Milnor, Morse Theory. Number 51, 1963.

U. Ozertem and D. Erdogmus, Locally defined principal curves and surfaces, The Journal of Machine Learning Research, vol.12, pp.1249-1286, 2011.

D. Svein-arne-pettersen, H. Johansen, V. Johansen, . Berg-johansen, A. Vamsidhar-reddy-gaddam et al., Soccer video and player position dataset, Proceedings of the 5th ACM Multimedia Systems Conference, pp.18-23, 2014.

J. M. Phillips, B. Wang, and Y. Zheng, Geometric inference on kernel density estimates. arXiv preprint, 2014.

B. L. Rao, Nonparametric Functional Estimation. Probability and Mathematical Statistics, 1983.

E. Schuster, Incorporating support constraints into nonparametric estimators of densities, Communications in Statistics - Theory and Methods, vol.9, issue.5, pp.1123-1136, 1958.
DOI : 10.1080/03610928508828965

R. Galen, J. A. Shorack, and . Wellner, Empirical processes with applications to statistics, SIAM, vol.59, 2009.

K. Bharath, K. Sriperumbudur, A. Fukumizu, . Gretton, R. Gert et al., Kernel choice and classifiability for rkhs embeddings of probability distributions, NIPS, pp.1750-1758, 2009.

R. Van-de-weygaert, G. Vegter, H. Edelsbrunner, J. Bernard, P. Jones et al., Alpha, Betti and the Megaparsec Universe: On the Topology of the Cosmic Web, In Transactions on Computational Science XIV, vol.722, issue.6, pp.60-101, 2011.
DOI : 10.1088/0004-637X/722/1/812

URL : https://hal.archives-ouvertes.fr/hal-01101279

W. Aad, . Van, and . Vaart, Asymptotic Statistics, Cambridge UP, vol.3, 2000.

W. Aad, . Van, J. A. Vaart, and . Wellner, Weak Convergence, 1996.

J. Yukich, Laws of large numbers for classes of functions, Journal of Multivariate Analysis, vol.17, issue.3, pp.245-260, 1985.
DOI : 10.1016/0047-259X(85)90083-1