Existence and consistency of Wasserstein barycenters
T Le Gouic, JM Loubes - Probability Theory and Related Fields, 2017 - Springer
Based on the Fréchet mean, we define a notion of barycenter corresponding to a usual
notion of statistical mean. We prove the existence of Wasserstein barycenters of random …
notion of statistical mean. We prove the existence of Wasserstein barycenters of random …
Distribution's template estimate with Wasserstein metrics
E Boissard, T Le Gouic, JM Loubes - 2015 - projecteuclid.org
In this paper, we tackle the problem of comparing distributions of random variables and
defining a mean pattern between a sample of random events. Using barycenters of …
defining a mean pattern between a sample of random events. Using barycenters of …
Characterization of barycenters in the Wasserstein space by averaging optimal transport maps
J Bigot, T Klein - ESAIM: Probability and Statistics, 2018 - esaim-ps.org
This paper is concerned by the study of barycenters for random probability measures in the
Wasserstein space. Using a duality argument, we give a precise characterization of the …
Wasserstein space. Using a duality argument, we give a precise characterization of the …
[PDF][PDF] Consistent estimation of a population barycenter in the Wasserstein space
J Bigot, T Klein - ArXiv e-prints, 2012 - perso.math.univ-toulouse.fr
We define a notion of barycenter for random probability measures in the Wasserstein space.
We study the population barycenter in terms of existence and uniqueness. Using a duality …
We study the population barycenter in terms of existence and uniqueness. Using a duality …
Integral approximation by kernel smoothing
B Delyon, F Portier - 2016 - projecteuclid.org
Abstract Let (X_1,...,X_n) be an iid sequence of random variables in R^d, d≧1. We show
that, for any function φ:R^d→R, under regularity conditions, n^1/2(n^-1i=1^nφ(X_i)f(X_i) …
that, for any function φ:R^d→R, under regularity conditions, n^1/2(n^-1i=1^nφ(X_i)f(X_i) …
Statistical properties of the quantile normalization method for density curve alignment
The article investigates the large sample properties of the quantile normalization method by
Bolstad et al.(2003)[4] which has become one of the most popular methods to align density …
Bolstad et al.(2003)[4] which has become one of the most popular methods to align density …
Estimation of translation, rotation, and scaling between noisy images using the Fourier–Mellin transform
In this paper we focus on extended Euclidean registration of a set of noisy images. We
provide an appropriate statistical model for this kind of registration problem, and a new …
provide an appropriate statistical model for this kind of registration problem, and a new …
Statistical methods for outlier detection in space telemetries
C Barreyre, L Boussouf, B Cabon, B Laurent… - Space Operations …, 2019 - Springer
Satellites monitoring is an important task to prevent the failure of satellites. For this purpose,
a large number of time series are analyzed in order to detect anomalies. In this paper, we …
a large number of time series are analyzed in order to detect anomalies. In this paper, we …
[HTML][HTML] Central limit theorem and bootstrap procedure for Wasserstein's variations with an application to structural relationships between distributions
E Del Barrio, P Gordaliza, H Lescornel… - Journal of Multivariate …, 2019 - Elsevier
Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are
used in many problems to analyze the homogeneity of collections of distributions and …
used in many problems to analyze the homogeneity of collections of distributions and …
Comparing time varying regression quantiles under shift invariance
Supplemental material contains detailed proofs of Theorems 3.1 and 3.2 as well as
Proposition 2.1, technical propositions E. 1, E. 2 and E. 3 and a discussion on the parameter …
Proposition 2.1, technical propositions E. 1, E. 2 and E. 3 and a discussion on the parameter …