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Volume 7 - Number 2 | July 2023

A prelude to statistics arising from optimal transport theory

Hung T. Nguyen

12/07/2023 106 67 0
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Multivariate quantiles Optimal transport Partial identification Random sets Wasserstein metrics

Abstract:

Purpose
This paper aims to offer a tutorial/introduction to new statistics arising from the theory of optimal transport to empirical researchers in econometrics and machine learning. Design/methodology/approach
Presenting in a tutorial/survey lecture style to help practitioners with the theoretical material. Findings
The tutorial survey of some main statistical tools (arising from optimal transport theory) should help practitioners to understand the theoretical background in order to conduct empirical research meaningfully. Originality/value
This study is an original presentation useful for new comers to the field.

References:

  1. Artstein, Z. (1983), “Distributions of random sets and random selections”, Israel Journal of Mathematics, Vol. 46, pp. 313-324.
  2. Belloni, A. and Winkler, R. (2011), “On multivariate quantiles under partial order”, The Annals of Statistics, Vol. 39 No. 2, pp. 1125-1179.
  3. Brenier, Y. (1991), “Polar factorization and monotone rearrangement of vector-valued functions”, Communications on Pure and Applied Mathematics, Vol. 44 No. 4, pp. 375-417.
  4. Breiman, L. (2001), “Statistical modeling: the two cultures”, Statistical Science, Vol. 16 No. 4, pp. 199-231.
  5. Carlier, G., Chernozukov, V. and Galichon, A. (2016), “Vector quantile regression: an optimal transport approach”, The Annals of Statistics, Vol. 44 No. 3, pp. 1165-1192.
  6. Carlier, G., Chernozukov, V. and Galichon, A. (2017), “Vector quantile regression beyond the specific case”, Journal of Multivariate Analysis, Vol. 161, pp. 96-102.
  7. Daoud, A. and Dubhashi, D. (2023), “Statistical modeling: the three cultures”. doi: 10.1162/99608f92.89f6fe66.
  8. Dudley, R.M. (2003), Real Analysis and Probability, Cambridge University Press, Cambridge, MA.
  9. Galichon, A. (2016), Optimal Transport Methods in Economics, Princeton Univ. Press., Princeton, NJ.
  10. Graf, S. and Mauldin, R.D. (1989), “A classification of disintegration of measures”, in Measure and Measurable Dynamics, No 94, Contemp.Math, pp. 147-158, AMS.
  11. Hallin, M., Paindaveine, D. and Siman, M. (2010), “Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to half-space depth”, The Annals of Statistics, Vol. 38 No. 2, pp. 635-669.
  12. Hartigan, J.A. (1987), “Estimation of a convex density contour in two dimensions”, Journal of the American Statistical Association, Vol. 82 No. 397, pp. 267-270.
  13. Kantorovich, L.V. (1942), “On the translocation of masses”, C.R. Academy of Sciences of URSS, Vol. 77, pp. 199-201.
  14. Koenker, R. (2017), “Quantile regression 40 years on”, Annual Review of Economics, Vol. 9 No. 1, pp. 155-176.
  15. Koenker, R. and Basett, G. (1978), “Regression quantiles”, Econometrica, Vol. 46, pp. 33-50.
  16. Manski, C. (2007), Identification for Prediction and Decision, Harvard University Press, Cambridge, MA.
  17. Matheron, G. (1975), Random Sets and Integral Geometry, J. Wiley, New York.
  18. McCam, R. (1995), “Existence and uniqueness of monotone measure-preserving maps”, Duke Math. J., Vol. 80 No. 2, pp. 309-323.
  19. Monge, G. (1781), “Memoire sur la theorie des deblais et des remblais”, in Histoire de l’ Academie Royale des Sciences de Paris, pp. 666-704.
  20. Nguyen, H.T. (2006), A Introduction to Random Sets, Chapman & Hall/CRC, Boca Raton, FL.
  21. Norberg, T. (1992), “On the existence of ordered coupling of random sets with applications”, Israel Journal of Mathematics, Vol. 77 No. 3, pp. 241-264.
  22. Parzen, E. (1979), “Nonparametric data modeling”, Journal of the American Statistical Association, Vol. 74 No. 365, pp. 105-121.
  23. Serfling, R. and Zuo, Y. (2010), “Discussion”, The Annals of Statistics, Vol. 38 No. 2, pp. 676-684.
  24. Villani, C. (2003), Topics in Optimal Transportation, American Mathematical Society, Providence, RI.

 

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