Fetching the paper…
Reading the bibliography…
Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.
1907
Earlier work this paper cites.
1908
Earlier work this paper cites.
1909
Earlier work this paper cites.
1909
Earlier work this paper cites.
1910
Earlier work this paper cites.
[author] Dvoretzky, AryehA., Kiefer, JackJ. and Wolfowitz, JacobJ. (1956). Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator. The Annals of Mathematical Statistics 27 642–669
1956
Earlier work this paper cites.
[author] Dudley, Richard MansfieldR. M. (1969). The Speed of Mean Glivenko-Cantelli Convergence. The Annals of Mathematical Statistics 40 40–50
1969
Earlier work this paper cites.
[author] Csorgo, MiklosM. and Revesz, PalP. (1978). Strong Approximations of the Quantile Process. The Annals of Statistics 6 882–894
1978
Earlier work this paper cites.
[author] Denker, ManfredM. (1985). Asymptotic Distribution Theory in Nonparametric Statistics. Braunschweig-Wiesbaden: Vieweg
1985
Earlier work this paper cites.
[author] Massart, PascalP. (1990). The Tight Constant in the Dvoretzky-Kiefer-Wolfowitz Inequality. The Annals of Probability 1269–1283
1990
Earlier work this paper cites.
[author] Efron, BradleyB. and Tibshirani, Robert J.R. J. (1994). An Introduction to the Bootstrap. CRC press
1994
Earlier work this paper cites.
[author] Gangbo, WilfridW. and McCann, Robert J.R. J. (1996). The Geometry of Optimal Transportation. Acta Mathematica 177 113–161
1996
Earlier work this paper cites.
[author] van der Vaart, Aad W.A. W. and Wellner, Jon A.J. A. (1996). Weak Convergence and Empirical Processes. Springer
1996
Earlier work this paper cites.
[author] Munk, AxelA. and Czado, ClaudiaC. (1998). Nonparametric Validation of Similar Distributions and Assessment of Goodness of Fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60 223–241
1998
Earlier work this paper cites.
[author] van der Vaart, AadA. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, UK ; New York, NY, USA
1998
Earlier work this paper cites.
[author] del Barrio, EustasioE., Cuesta-Albertos, Juan A.J. A., Matrán, CarlosC. and Rodríguez-Rodríguez, Jes{\’u}s M.J. M. (1999). Tests of Goodness of Fit Based on the L 2 L_{2} -Wasserstein Distance. The Annals of Statistics 27 1230–1239
1999
Earlier work this paper cites.
[author] Pollard, DavidD. (2002). A User’s Guide to Measure Theoretic Probability 8. Cambridge University Press
2002
Earlier work this paper cites.
Bousquet, O
2003
Earlier work this paper cites.
[author] Freitag, G.G., Munk, A.A. and Vogt, M.M. (2003). Assessing Structural Relationships between Distributions-a Quantile Process Approach Based on Mallows Distance. In Recent Advances and Trends in Nonparametric Statistics 123–137. Elsevier
2003
Earlier work this paper cites.
[author] Villani, CédricC. (2003). Topics in Optimal Transportation. American Mathematical Soc
2003
Earlier work this paper cites.
[author] del Barrio, EustasioE., Giné, EvaristE. and Utzet, FredericF. (2005). Asymptotics for L 2 L^{2} Functionals of the Empirical Quantile Process, with Applications to Tests of Fit Based on Weighted Wasserstein Distances. Bernoulli 11 131–189
2005
Earlier work this paper cites.
[author] Freitag, GudrunG. and Munk, AxelA. (2005). On Hadamard Differentiability in k k –Sample Semiparametric Models—with Applications to the Assessment of Structural Relationships. Journal of Multivariate Analysis 94 123–158
2005
Earlier work this paper cites.
[author] Giné, EvaristE. and Koltchinskii, VladimirV. (2006). Concentration Inequalities and Asymptotic Results for Ratio Type Empirical Processes. The Annals of Probability 34 1143–1216
2006
Earlier work this paper cites.
[author] Bogachev, Vladimir IgorevichV. I. (2007). Measure Theory 1. Springer-Verlag, Berlin, Germany
2007
Earlier work this paper cites.
[author] Bouchitté, GuyG., Jimenez, ChloéC. and Rajesh, M.M. (2007). A New L ∞ L^{\infty} Estimate in Optimal Mass Transport. Proceedings of the American Mathematical Society 135 3525–3535
2007
Earlier work this paper cites.
[author] Freitag, GudrunG., Czado, ClaudiaC. and Munk, AxelA. (2007). A Nonparametric Test for Similarity of Marginals—With Applications to the Assessment of Population Bioequivalence. Journal of Statistical Planning and Inference 137 697–711
2007
Earlier work this paper cites.
2007
Cited alongside, same era.
[author] Álvarez-Esteban, Pedro CésarP. C., Del Barrio, EustasioE., Cuesta-Albertos, Juan AntonioJ. A. and Matran, CarlosC. (2008). Trimmed Comparison of Distributions. Journal of the American Statistical Association 103 697–704
2008
Cited alongside, same era.
[author] Tsybakov, Alexandre B.A. B. (2008). Introduction to Nonparametric Estimation. Springer Science & Business Media
2008
Cited alongside, same era.
[author] Shorack, Galen R.G. R. and Wellner, Jon A.J. A. (2009). Empirical Processes with Applications to Statistics. SIAM
2009
Cited alongside, same era.
[author] Stein, Elias M.E. M. and Shakarchi, RamiR. (2009). Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press
[author] Sommerfeld, MaxM. and Munk, AxelA. (2018). Inference for Empirical Wasserstein Distances on Finite Spaces. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 80 219–238
2018
Later among the works it cites.
[author] Bobkov, SergeyS. and Ledoux, MichelM. (2019). One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances. Memoirs of the American Mathematical Society 261
2019
Closest in time.
[author] Chen, QihuiQ. and Fang, ZhengZ. (2019). Inference on Functionals under First Order Degeneracy. Journal of Econometrics 210 459–481
2019
Closest in time.
[author] del Barrio, EustasioE., Gordaliza, PaulaP. and Loubes, Jean-MichelJ.-M. (2019). A Central Limit Theorem for Lp Transportation Cost on the Real Line with Application to Fairness Assessment in Machine Learning. Information and Inference: A Journal of the IMA 8 817–849
2019
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2009
Cited alongside, same era.
[author] Bonassi, Fernando V.F. V., You, LingchongL. and West, MikeM. (2011). Bayesian Learning from Marginal Data in Bionetwork Models. Statistical Applications in Genetics and Molecular Biology 10
2011
Cited alongside, same era.
Rabin, J
2011
Cited alongside, same era.
[author] Shao, JunJ. and Tu, DongshengD. (2012). The Jackknife and Bootstrap. Springer Science & Business Media
2012
Cited alongside, same era.
[author] Bonnotte, NicolasN. (2013). Unidimensional and Evolution Methods for Optimal Transportation, PhD thesis, Paris 11
2013
Cited alongside, same era.
[author] Diaconis, PersiP., Holmes, SusanS. and Shahshahani, MehrdadM. (2013). Sampling from a Manifold. In Advances in Modern Statistical Theory and Applications: A Festschrift in Honor of Morris L. Eaton 102–125. Institute of Mathematical Statistics
2013
Cited alongside, same era.
[author] Nguyen, XuanLongX. (2013). Convergence of Latent Mixing Measures in Finite and Infinite Mixture Models. The Annals of Statistics 41 370–400
2013
Cited alongside, same era.
[author] Revuz, DanielD. and Yor, MarcM. (2013). Continuous Martingales and Brownian Motion 293. Springer Science & Business Media
2013
Cited alongside, same era.
[author] del Barrio, EustasioE. and Loubes, Jean-MichelJ.-M. (2019). Central Limit Theorems for Empirical Transportation Cost in General Dimension. The Annals of Probability 47 926–951
2019
Closest in time.
Deshpande, I
2019
Closest in time.
Kolouri, S
2019
Closest in time.
Paty, F.-P
2019
Closest in time.
[author] Peyré, GabrielG. and Cuturi, MarcoM. (2019). Computational Optimal Transport. Foundations and Trends® in Machine Learning 11 355–607
2019
Closest in time.
2019
Closest in time.
[author] Tameling, CarlaC., Sommerfeld, MaxM. and Munk, AxelA. (2019). Empirical Optimal Transport on Countable Metric Spaces: Distributional Limits and Statistical Applications. The Annals of Applied Probability 29 2744–2781
2019
Closest in time.
[author] Verdinelli, IsabellaI. and Wasserman, LarryL. (2019). Hybrid Wasserstein Distance and Fast Distribution Clustering. Electronic Journal of Statistics 13 5088–5119
2019
Closest in time.
[author] Berthet, PhilippeP., Fort, Jean-ClaudeJ.-C. and Klein, ThierryT. (2020). A Central Limit Theorem for Wasserstein Type Distances between Two Distinct Univariate Distributions. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 56 954–982
2020
Closest in time.
[author] Brehmer, JohannJ., Kling, FelixF., Espejo, IrinaI. and Cranmer, KyleK. (2020). MadMiner: Machine Learning-Based Inference for Particle Physics. Computing and Software for Big Science 4 1–25
2020
Closest in time.
Dalmasso, N
2020
Closest in time.
Dalmasso, N
2020
Closest in time.
[author] Kim, IlmunI., Balakrishnan, SivaramanS. and Wasserman, LarryL. (2020). Robust Multivariate Nonparametric Tests via Projection Averaging. The Annals of Statistics 48 3417–3441
2020
Closest in time.
[author] Klatt, MarcelM., Tameling, CarlaC. and Munk, AxelA. (2020). Empirical Regularized Optimal Transport: Statistical Theory and Applications. SIAM Journal on Mathematics of Data Science 2 419–443
2020
Closest in time.
[author] Lei, JingJ. (2020). Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces. Bernoulli 26 767–798
2020
Closest in time.
Nadjahi, K
2020
Closest in time.
Nguyen, K
2020
Closest in time.
2021
Closest in time.
[author] Ebert, AnthonyA., Dutta, RitabrataR., Mengersen, KerrieK., Mira, AntoniettaA., Ruggeri, FabrizioF. and Wu, PaulP. (2021). Likelihood-Free Parameter Estimation for Dynamic Queueing Networks: Case Study of Passenger Flow in an International Airport Terminal. Journal of the Royal Statistical Society: Series C (Applied Statistics) 70 770–792
2021
Closest in time.
2021
Closest in time.