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
Geodesic PCA in the Wasserstein space by convex PCA, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.53, issue.1, pp.1-26, 2017. ,
DOI : 10.1214/15-AIHP706
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
Characterization of barycenters in the Wasserstein space by averaging optimal transport maps, ESAIM: Probability and Statistics, 2017. ,
DOI : 10.1051/ps/2017020
URL : https://hal.archives-ouvertes.fr/hal-00763668
One-dimensional empirical measures, order statistics and Kantorovich transport distances. Memoirs of the Available at https, 2017. ,
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/pdf/1111.5927
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
Dimensionality reduction when data are density functions, Computational Statistics & Data Analysis, vol.55, issue.1, pp.401-420, 2011. ,
DOI : 10.1016/j.csda.2010.05.008
LesélémentsLeséléments aléatoires de nature quelconque dans un espace distancié, Ann. Inst. H.Poincaré, Sect. B, Prob. et Stat, vol.10, pp.235-310, 1948. ,
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
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, 2010. ,
DOI : 10.1214/10-AOS813
Functional data analysis for density functions by transformation to a Hilbert space, The Annals of Statistics, vol.44, issue.1, pp.183-218771, 2016. ,
DOI : 10.1214/15-AOS1363SUPP
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
An Introduction to Partial Differential Equations, Texts in Applied Mathematics, vol.13, 1993. ,
Introduction to nonparametric estimation, 2009. ,
Topics in Optimal Transportation, Graduate Studies in Mathematics, vol.58, 2003. ,
Alignment of curves by dynamic time warping, Annals of Statistics, vol.25, issue.3, pp.1251-1276, 1997. ,
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 : 10.4171/RLM/506
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