G. [. Agueh and . Carlier, Barycenters in the Wasserstein Space, SIAM Journal on Mathematical Analysis, vol.43, issue.2, pp.904-924, 2011.
DOI : 10.1137/100805741
URL : https://hal.archives-ouvertes.fr/hal-00637399

J. Bigot, R. Gouet, T. Klein, and A. Lopez, Geodesic PCA in the Wasserstein space by Convex PCA. Annales de l'Institut Henri Poincaré B: Probability and Statistics, 2015.

B. M. Bolstad, R. A. Irizarry, M. Astrand, and T. P. Speed, A comparison of normalization methods for high density oligonucleotide array data based on variance and bias, Bioinformatics, vol.19, issue.2, pp.185-193, 2003.
DOI : 10.1093/bioinformatics/19.2.185

T. [. Bigot and . Klein, Characterization of barycenters in the Wasserstein space by averaging optimal transport maps, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00763668

M. [. Bobkov and . Ledoux, One-dimensional empirical measures, order statistics and Kantorovich transport distances Book in preparation, 2014.

T. [. Boissard, J. Gouic, and . Loubes, Distribution???s template estimate with Wasserstein metrics, Bernoulli, vol.21, issue.2, pp.740-759, 2015.
DOI : 10.3150/13-BEJ585
URL : http://arxiv.org/abs/1111.5927

E. Del-barrio, E. Giné, and F. Utzet, Asymptotics for L 2 functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances, Bernoulli, vol.11, issue.1, pp.131-189, 2005.
DOI : 10.3150/bj/1110228245

]. P. Del11 and . Delicado, Dimensionality reduction when data are density functions, Comput. Statist. Data Anal, vol.55, issue.1, pp.401-420, 2011.

M. Fréchet, LesélémentsLeséléments aléatoires de nature quelconque dans un espace distancié, Ann. Inst. H.Poincaré, Sect. B, Prob. et Stat, vol.10, pp.235-310, 1948.

K. [. Kneip, Inference for Density Families Using Functional Principal Component Analysis, Journal of the American Statistical Association, vol.96, issue.454, pp.519-542, 2001.
DOI : 10.1198/016214501753168235

T. [. Li and . Hsing, Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data, The Annals of Statistics, vol.38, issue.6, pp.3321-3351
DOI : 10.1214/10-AOS813

H. [. Petersen and . Müller, Functional data analysis for density functions by transformation to a Hilbert space Annals of Statistics, To be published, 2015. [PZ16] V.M. Panaretos and Y. Zemel. Amplitude and phase variation of point processes, Annals of Statistics, vol.44, issue.2, pp.771-812, 2016.

J. O. Ramsay and X. Li, Curve registration, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.60, issue.2, pp.243-259, 2001.
DOI : 10.1111/1467-9868.00129

]. A. Tsy09 and . Tsybakov, Introduction to nonparametric estimation Springer Series in Statistics, 2009.

]. C. Vil03 and . Villani, Topics in Optimal Transportation, Graduate Studies in Mathematics, vol.58, 2003.

T. [. Wang and . Gasser, Alignment of curves by dynamic time warping, Annals of Statistics, vol.25, issue.3, pp.1251-1276, 1997.

A. [. Wu and . Srivastava, An information-geometric framework for statistical inferences in the neural spike train space, Journal of Computational Neuroscience, vol.9, issue.54, pp.725-748, 2011.
DOI : 10.1007/s10827-011-0336-x

H. [. Zhang and . Müller, Functional density synchronization, Computational Statistics & Data Analysis, vol.55, issue.7, pp.2234-2249, 2011.
DOI : 10.1016/j.csda.2011.01.007
URL : http://anson.ucdavis.edu/~mueller/fdw16.pdf