Fetching the paper…
Reading the bibliography…
In this paper we study multivariate ranks and quantiles, defined using the theory of optimal transport, and build on the work of Chernozhukov et al.(2017) and Hallin et al.(2021).
1905
Earlier work this paper cites.
1909
Earlier work this paper cites.
1909
Earlier work this paper cites.
[author] Blomqvist, NilsN. (1950). On a measure of dependence between two random variables. Ann. Math. Statistics 21 593–600. 10.1214/aoms/1177729754 0039190
1950
Earlier work this paper cites.
[author] Hoeffding, WassilyW. (1952). The large-sample power of tests based on permutations of observations. Ann. Math. Statistics 23 169–192. 10.1214/aoms/1177729436 57521
1952
Earlier work this paper cites.
[author] Weiss, LionelL. (1960). Two-sample tests for multivariate distributions. Ann. Math. Statist. 31 159–164. 10.1214/aoms/1177705995 0119305
1960
Earlier work this paper cites.
[author] Blum, J. R.J. R., Kiefer, J.J. and Rosenblatt, M.M. (1961). Distribution free tests of independence based on the sample distribution function. Ann. Math. Statist. 32 485–498. 10.1214/aoms/1177705055 0125690
1961
Earlier work this paper cites.
[author] Bickel, P. J.P. J. (1968). A distribution free version of the Smirnov two sample test in the p p -variate case. Ann. Math. Statist. 40 1–23. 10.1214/aoms/1177697800 0256519
1968
Earlier work this paper cites.
[author] Rockafellar, R. TyrrellR. T. (1970). Convex analysis. Princeton Mathematical Series, No. 28. Princeton University Press, Princeton, N.J. 0274683
1970
Earlier work this paper cites.
[author] Lehmann, E. L.E. L. (1975). Nonparametrics: statistical methods based on ranks. Holden-Day, Inc., San Francisco, Calif.; McGraw-Hill International Book Co., New York-Düsseldorf With the special assistance of H. J. M. d’Abrera, Holden-Day Series in Probability and Statistics. 0395032
1975
Earlier work this paper cites.
[author] Friedman, Jerome H.J. H. and Rafsky, Lawrence C.L. C. (1979). Multivariate generalizations of the Wald-Wolfowitz and Smirnov two-sample tests. Ann. Statist. 7 697–717. 532236
1979
Earlier work this paper cites.
[author] Oja, HannuH. (1983). Descriptive statistics for multivariate distributions. Statist. Probab. Lett. 1 327–332. 10.1016/0167-7152(83)90054-8 721446
1983
Earlier work this paper cites.
[author] Ajtai, M.M., Komlós, J.J. and Tusnády, G.G. (1984). On optimal matchings. Combinatorica 4 259–264
1984
Earlier work this paper cites.
[author] Schilling, Mark F.M. F. (1986). Multivariate two-sample tests based on nearest neighbors. J. Amer. Statist. Assoc. 81 799–806. 860514
1986
Earlier work this paper cites.
[author] Aurenhammer, F.F. (1987). Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16 78–96. 10.1137/0216006 873251
1987
Earlier work this paper cites.
[author] Oliker, V. I.V. I. and Prussner, L. D.L. D. (1988). On the numerical solution of the equation ( ∂ 2 z / ∂ x 2 ) ( ∂ 2 z / ∂ y 2 ) − ( ( ∂ 2 z / ∂ x ∂ y ) ) 2 = f (\partial^{2}z/\partial x^{2})(\partial^{2}z/\partial y^{2})-((\partial^{2}z/\partial x\partial y))^{2}=f and its discretizations. I. Numer. Math. 54 271–293. 10.1007/BF01396762 971703
1988
Earlier work this paper cites.
[author] Caffarelli, Luis A.L. A. (1990). Interior W 2 , p W^{2,p} estimates for solutions of the Monge-Ampère equation. Ann. of Math. (2) 131 135–150. 10.2307/1971510 1038360
1990
Earlier work this paper cites.
[author] Liu, Regina Y.R. Y. (1990). On a notion of data depth based on random simplices. Ann. Statist. 18 405–414. 10.1214/aos/1176347507 1041400
1990
Earlier work this paper cites.
[author] Brenier, YannY. (1991). Polar factorization and monotone rearrangement of vector-valued functions. Comm. Pure Appl. Math. 44 375–417. 10.1002/cpa.3160440402 1100809
1991
Earlier work this paper cites.
[author] Caffarelli, Luis A.L. A. (1992). The regularity of mappings with a convex potential. J. Amer. Math. Soc. 5 99–104
1992
Earlier work this paper cites.
[author] Caffarelli, Luis A.L. A. (1992). Boundary regularity of maps with convex potentials. Comm. Pure Appl. Math. 45 1141–1151
1992
Earlier work this paper cites.
[author] Cuesta-Albertos, J. A.J. A., Rüschendorf, L.L. and Tuero-Díaz, A.A. (1993). Optimal coupling of multivariate distributions and stochastic processes. J. Multivariate Anal. 46 335–361. 10.1006/jmva.1993.1064 1240428
1993
Earlier work this paper cites.
[author] Hörmander, LarsL. (1994). Notions of convexity. Progress in Mathematics 127. Birkhäuser Boston, Inc., Boston, MA. 1301332
1994
Earlier work this paper cites.
[author] McCann, Robert J.R. J. (1995). Existence and uniqueness of monotone measure-preserving maps. Duke Math. J. 80 309–323. 10.1215/S0012-7094-95-08013-2 1369395
1995
Earlier work this paper cites.
[author] Caffarelli, Luis A.L. A. (1996). Boundary regularity of maps with convex potentials. II. Ann. of Math. (2) 144 453–496
1996
Earlier work this paper cites.
[author] Chaudhuri, ProbalP. (1996). On a geometric notion of quantiles for multivariate data. J. Amer. Statist. Assoc. 91 862–872. 10.2307/2291681 1395753
1996
Earlier work this paper cites.
[author] Gangbo, WilfridW. and McCann, Robert J.R. J. (1996). The geometry of optimal transportation. Acta Math. 177 113–161. 10.1007/BF02392620 1440931
1996
Earlier work this paper cites.
[author] Caffarelli, Luis A.L. A., Kochengin, Sergey A.S. A. and Oliker, Vladimir I.V. I. (1999). On the numerical solution of the problem of reflector design with given far-field scattering data. In Monge Ampère equation: applications to geometry and optimization (Deerfield Beach, FL, 1997). Contemp. Math. 226 13–32. Amer. Math. Soc., Providence, RI. 10.1090/conm/226/03233 1660740
1997
Earlier work this paper cites.
[author] Gangbo, WilfridW. (1999). The Monge mass transfer problem and its applications. In Monge Ampère equation: applications to geometry and optimization (Deerfield Beach, FL, 1997). Contemp. Math. 226 79–104. Amer. Math. Soc., Providence, RI. 10.1090/conm/226/03236 1660743
1997
Earlier work this paper cites.
[author] Koltchinskii, V. I.V. I. (1997). M M -estimation, convexity and quantiles. Ann. Statist. 25 435–477. 10.1214/aos/1031833659 1439309
1997
Earlier work this paper cites.
[author] Aurenhammer, FranzF., Hoffmann, FriedrichF. and Aronov, BorisB. (1998). Minkowski-type theorems and least-squares clustering. Algorithmica 20 61–76
1998
Earlier work this paper cites.
[author] van der Vaart, A. W.A. W. (1998). Asymptotic statistics. Cambridge Series in Statistical and Probabilistic Mathematics 3. Cambridge University Press, Cambridge. 10.1017/CBO9780511802256 1652247
1998
Earlier work this paper cites.
[author] Hollander, MylesM. and Wolfe, Douglas A.D. A. (1999). Nonparametric statistical methods, second ed. Wiley Series in Probability and Statistics: Texts and References Section. John Wiley & Sons, Inc., New York A Wiley-Interscience Publication. 1666064
1999
Earlier work this paper cites.
[author] Rousseeuw, Peter J.P. J. and Ruts, IdaI. (1999). The depth function of a population distribution. Metrika 49 213–244. 10.1007/PL00020903
1999
Earlier work this paper cites.
[author] Dudley, R. M.R. M. (2002). Real analysis and probability. Cambridge University Press, New York
2002
Earlier work this paper cites.
2003
Cited alongside, same era.
[author] Hallin, MarcM. and Werker, Bas J. M.B. J. M. (2003). Semi-parametric efficiency, distribution-freeness and invariance. Bernoulli 9 137–165. 10.3150/bj/1068129013 1963675
2003
Cited alongside, same era.
2003
Cited alongside, same era.
2003
Cited alongside, same era.
[author] Lévy, BrunoB. (2015). A numerical algorithm for L 2 L_{2} semi-discrete optimal transport in 3D. ESAIM Math. Model. Numer. Anal. 49 1693–1715. 10.1051/m2an/2015055 3423272
2015
Later among the works it cites.
[author] Galichon, AlfredA. (2016). Optimal transport methods in economics. Princeton University Press, Princeton, NJ. 10.1515/9781400883592 3586373
2016
Later among the works it cites.
[author] Gu, XianfengX., Luo, FengF., Sun, JianJ. and Yau, Shing-TungS.-T. (2016). Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge-Ampere equations. Asian J. Math. 20 383–398. 10.4310/AJM.2016.v20.n2.a7 3480024
2016
Later among the works it cites.
[author] Gutiérrez, C. E.C. E. (2016). The Monge-Ampère equation. Progress in Nonlinear Differential Equations and their Applications 89. Birkhäuser/Springer, [Cham] Second edition [of MR1829162]
2016
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
[author] Villani, CédricC. (2003). Topics in optimal transportation. Graduate Studies in Mathematics 58. American Mathematical Society, Providence, RI. 10.1007/b12016 1964483
2003
Cited alongside, same era.
2003
Cited alongside, same era.
[author] Baringhaus, L.L. and Franz, C.C. (2004). On a new multivariate two-sample test. J. Multivariate Anal. 88 190–206. 10.1016/S0047-259X(03)00079-4 2021870
2004
Cited alongside, same era.
2004
Cited alongside, same era.
[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. 10.3150/bj/1110228245 2121458
2005
Cited alongside, same era.
[author] Lehmann, E. L.E. L. and Romano, Joseph P.J. P. (2005). Testing statistical hypotheses, third ed. Springer Texts in Statistics. Springer, New York. 2135927
2005
Cited alongside, same era.
[author] Rosenbaum, Paul R.P. R. (2005). An exact distribution-free test comparing two multivariate distributions based on adjacency. J. R. Stat. Soc. Ser. B Stat. Methodol. 67 515–530. 10.1111/j.1467-9868.2005.00513.x 2168202
2005
Cited alongside, same era.
2007
Cited alongside, same era.
[author] Chernozhukov, VictorV., Galichon, AlfredA., Hallin, MarcM. and Henry, MarcM. (2017). Monge-Kantorovich depth, quantiles, ranks and signs. Ann. Statist. 45 223–256. 10.1214/16-AOS1450 3611491
2017
Later among the works it cites.
[author] Figalli, A.A. (2017). The Monge-Ampére equation and its application. Zurich lectures in advanced mathematics 58. European Mathematical Society
2017
Later among the works it cites.
2017
Later among the works it cites.
[author] Ramdas, AadityaA., García Trillos, NicolásN. and Cuturi, MarcoM. (2017). On Wasserstein two-sample testing and related families of nonparametric tests. Entropy 19 Paper No. 47, 15. 10.3390/e19020047 3608466
2017
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.
[author] del Barrio, EustasioE., Gordaliza, PaulaP., Lescornel, HélèneH. and Loubes, Jean-MichelJ.-M. (2019). Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions. J. Multivariate Anal. 169 341–362. 10.1016/j.jmva.2018.09.014 3875604
2018
Later among the works it cites.
[author] Figalli, AlessioA. (2018). On the continuity of center-outward distribution and quantile functions. Nonlinear Anal. 177 413–421. 10.1016/j.na.2018.05.008 3886582
2018
Later among the works it cites.
[author] Pfister, NiklasN., Bühlmann, PeterP., Schölkopf, BernhardB. and Peters, JonasJ. (2018). Kernel-based tests for joint independence. J. R. Stat. Soc. Ser. B. Stat. Methodol. 80 5–31. 10.1111/rssb.12235 3744710
2018
Later among the works it cites.
[author] Rigollet, PhilippeP. and Weed, JonathanJ. (2018). Entropic optimal transport is maximum-likelihood deconvolution. C. R. Math. Acad. Sci. Paris 356 1228–1235. 10.1016/j.crma.2018.10.010 3907589
2018
Later among the works it cites.
[author] Weihs, L.L., Drton, M.M. and Meinshausen, N.N. (2018). Symmetric rank covariances: a generalized framework for nonparametric measures of dependence. Biometrika 105 547–562. 10.1093/biomet/asy021 3842884
2018
Later among the works it cites.
[author] Berrett, T. B.T. B. and Samworth, R. J.R. J. (2019). Nonparametric independence testing via mutual information. Biometrika 106 547–566. 10.1093/biomet/asz024 3992389
2019
Closest in time.
[author] Bobkov, SergeyS. and Ledoux, MichelM. (2019). One-dimensional empirical measures, order statistics, and Kantorovich transport distances. Mem. Amer. Math. Soc. 261 v+126. 10.1090/memo/1259 4028181
2019
Closest in time.
[author] Cordero-Erausquin, DarioD. and Figalli, AlessioA. (2019). Regularity of monotone transport maps between unbounded domains. Discrete Contin. Dyn. Syst. 39 7101–7112. 10.3934/dcds.2019297 4026183
2019
Closest in time.
[author] del Barrio, EustasioE. and Loubes, Jean-MichelJ.-M. (2019). Central limit theorems for empirical transportation cost in general dimension. Ann. Probab. 47 926–951. 10.1214/18-AOP1275 3916938
2019
Closest in time.
[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.
[author] Kitagawa, JunJ. and McCann, RobertR. (2019). Free discontinuities in optimal transport. Arch. Ration. Mech. Anal. 232 1505–1541. 10.1007/s00205-018-01348-3 3928755
2019
Closest in time.
[author] Kitagawa, JunJ., Mérigot, QuentinQ. and Thibert, BorisB. (2019). Convergence of a Newton algorithm for semi-discrete optimal transport. J. Eur. Math. Soc. (JEMS) 21 2603–2651. 10.4171/JEMS/889 3985609
2019
Closest in time.
[author] Móri, Tamás F.T. F. and Székely, Gábor J.G. J. (2019). Four simple axioms of dependence measures. Metrika 82 1–16. 10.1007/s00184-018-0670-3 3897521
2019
Closest in time.
[author] Panaretos, Victor M.V. M. and Zemel, YoavY. (2019). Statistical aspects of Wasserstein distances. Annu. Rev. Stat. Appl. 6 405–431. 10.1146/annurev-statistics-030718-104938 3939527
2019
Closest in time.
[author] Peyré, GabrielG., Cuturi, MarcoM. et al. (2019). Computational Optimal Transport: With Applications to Data Science. Foundations and Trends® in Machine Learning 11 355–607
2019
Closest in time.
[author] Rigollet, PhilippeP. and Weed, JonathanJ. (2019). Uncoupled isotonic regression via minimum Wasserstein deconvolution. Inf. Inference 8 691–717. 10.1093/imaiai/iaz006 4045481
2019
Closest in time.
[author] Weed, JonathanJ. and Bach, FrancisF. (2019). Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance. Bernoulli 25 2620–2648. 10.3150/18-BEJ1065 4003560
2019
Closest in time.
[author] Zemel, YoavY. and Panaretos, Victor M.V. M. (2019). Fréchet means and Procrustes analysis in Wasserstein space. Bernoulli 25 932–976. 10.3150/17-bej1009 3920362
2019
Closest in time.
[author] Chizat, LenaicL., Roussillon, PierreP., Léger, FlavienF., Vialard, François-XavierF.-X. and Peyré, GabrielG. (2020). Faster Wasserstein Distance Estimation with the Sinkhorn Divergence. Advances in Neural Information Processing Systems 33
2020
Closest in time.
[author] del Barrio, EustasioE., González-Sanz, AlbertoA. and Hallin, MarcM. (2020). A note on the regularity of optimal-transport-based center-outward distribution and quantile functions. J. Multivariate Anal. 180 104671, 13. 10.1016/j.jmva.2020.104671 4147635
2020
Closest in time.
[author] Klatt, MarcelM., Tameling, CarlaC. and Munk, AxelA. (2020). Empirical regularized optimal transport: statistical theory and applications. SIAM J. Math. Data Sci. 2 419–443. 10.1137/19M1278788 4105566
2020
Closest in time.
2021
Closest in time.
[author] Hallin, MarcM., del Barrio, EustasioE., Cuesta-Albertos, JuanJ. and Matrán, CarlosC. (2021). Distribution and quantile functions, ranks and signs in dimension d d : A measure transportation approach. The Annals of Statistics 49 1139–1165
2021
Closest in time.
[author] Gretton, A.A., Herbrich, R.R., Smola, A.A., Bousquet, O.O. and Schölkopf, B.B. (2005). Kernel methods for measuring independence. J. Mach. Learn. Res. 6 2075–2129 (electronic). 2249882
2075
Closest in time.