On Some Goodness of Fit Tests for Normality Based on the Optimal Transport Distance

• Autorzy: Mazur Marcin , Kościelniak Piotr

Identyfikatory

DOI

10.4467/20838476SI.18.005.10410

• Języki publikacji: EN

Abstrakty

EN

We apply the optimal transport distance to construct two goodness of t tests for (univariate) normality. The derived statistics are then compared with those used by the Shapiro-Wilk, the Anderson-Darling and the Cramervon Mises tests. In particular, we preform Monte Carlo experiments, involving computations of the test power against some selected alternatives and wide range of sample sizes, which show eciency of the obtained test procedures.

Słowa kluczowe

EN

goodness of fit test (for normality); optimal transport distance; Wasserstein distance; autoencoder-based generative model

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2018
• Tom: Vol. 27
• Strony: 59--68
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Mazur Marcin

• Jagiellonian University Faculty of Mathematics and Computer Science Lojasiewicza 6, 30-348 Krakow, Poland

autor

Kościelniak Piotr

• Jagiellonian University Faculty of Mathematics and Computer Science Lojasiewicza 6, 30-348 Krakow, Poland

Bibliografia

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• [2] F. Bretz, T. Hothorn, and P. Westfall. Multiple Comparisons Using R. CRC Press, Boca Raton, 2010.
• [3] E. del Barrio, J.A Cuesta-Albertos, C. Matrán, and Rodríguez-Rodríguez J.M. Tests of goodness of t based on the l2-wasserstein distance. The Annals of Statistics, 27:1230-1239, 1999.
• [4] S. Kolouri, P.E. Pope, C.E. Martin, and G.K. Rohde. Sliced wasserstein autoencoders. In ICLR, 2019.
• [5] E. Krauczí. A study of the quantile correlation test for normality. Test, 18:156-165, 2009.
• [6] G. Monge. Mémoire sur la théorie des déblais et des remblais. De lÍmprimerie Royale, Paris, 1781.
• [7] A. Palmer, D. Dey, and J. Bi. Reforming generative autoencoders via goodnessof-fit hypothesis testing. In UAI, 2018.
• [8] S.T. Rachev and L. Rüschendorf. Mass Transportation Problems, Volume I: Theory. Springer, New York, 1998.
• [9] I. Tolstikhin, O. Bousquet, S. Gelly, and B. Schoelkopf. Wasserstein autoencoders. In ICLR, 2018.
• [10] C. Villani. Optimal Transport: Old and New. Springer, Berlin, 2008.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).