Geodesic
Statistical tests for uniformity of distribution and independence of vectors based on pairwise distances
Matematičeskie voprosy kriptografii, Tome 14 (2023), pp. 55-70.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of testing statistical hypotheses on the uniformity of distribution and independence of random vectors is interesting from theoretical and practical viewpoints. Many authors had proposed various approaches to solving it. In some tests for the hypotheses on the uniformity of distributions of random vectors in a multidimensional region or on their independence some functions of pairwise distances between sample points are used as statistics. The paper contains a brief review of such tests. A new test for the hypothesis on the uniformity of distribution based on pairwise distances is proposed. 
@article{MVK_2023_14_a2,
     author = {A. M. Zubkov},
     title = {Statistical tests for uniformity of distribution and independence of vectors based on pairwise distances},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {55--70},
     publisher = {mathdoc},
     volume = {14},
     year = {2023},
     language = {ru},
     url = {https://geodesic-test.mathdoc.fr/item/MVK_2023_14_a2/}
}
TY  - JOUR
AU  - A. M. Zubkov
TI  - Statistical tests for uniformity of distribution and independence of vectors based on pairwise distances
JO  - Matematičeskie voprosy kriptografii
PY  - 2023
SP  - 55
EP  - 70
VL  - 14
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/MVK_2023_14_a2/
LA  - ru
ID  - MVK_2023_14_a2
ER  - 
%0 Journal Article
%A A. M. Zubkov
%T Statistical tests for uniformity of distribution and independence of vectors based on pairwise distances
%J Matematičeskie voprosy kriptografii
%D 2023
%P 55-70
%V 14
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/MVK_2023_14_a2/
%G ru
%F MVK_2023_14_a2
A. M. Zubkov. Statistical tests for uniformity of distribution and independence of vectors based on pairwise distances. Matematičeskie voprosy kriptografii, Tome 14 (2023), pp. 55-70. https://geodesic-test.mathdoc.fr/item/MVK_2023_14_a2/

[1] Bakirov N.K., Rizzo M.L., Székely G.J., “A multivariate nonparametric test of independence”, J. Multivar. Anal., 97 (2006), 1742–1756 | DOI | MR | Zbl

[2] Bartoszyński R., Pearl D.K., Lawrence J., “A multidimensional goodness-of-fit test based on interpoint distances”, J. Amer. Statist. Assoc., 92(438) (1997), 577–586 | MR | Zbl

[3] Berrendero J., Cuevas A., Vasquez F., “Testing multivariate uniformity: the distance-to-boundary method”, Canad. J. Statist., 34 (2006), 693–707 | DOI | MR | Zbl

[4] Berrendero J., Cuevas A., Pateiro-Lopez B., “A multivariate uniformity test for the case of unknown support”, Statistics and Computing, 22 (2012), 259–271 | DOI | MR | Zbl

[5] Berrendero J., Cuevas A., Pateiro-Lopez B., “Testing uniformity for the case of a planar unknown support”, Canad. J. Statist., 40 (2012), 378–395 | DOI | MR | Zbl

[6] Bickel P.J., Breiman L., “Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test”, Ann. Probab., 11:1 (1983), 185–214 | DOI | MR | Zbl

[7] Ebner B., Henze N., Yukich J.E., “Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances”, J. Multivar. Anal., 165 (2018), 231–242 | DOI | MR | Zbl

[8] Jain A., Xu X., Ho T., Xiao F., “Uniformity testing using minimal spanning tree”, Proc. 16th Int. Conf. Pattern Recognition, v. 4, 2002, 281–284 | DOI

[9] Jammalamadaka S. R., Zhou S., “Goodness of fit in multidimensions based on nearest neighbor distances”, J. Nonparam. Statist., 2 (1993), 271–284 | DOI | MR | Zbl

[10] Janson S., “Maximal spacings in several dimensions”, Ann. Probab., 15:1 (1987), 274–280 | DOI | MR | Zbl

[11] Gretton A., Györfi L., “Consistent nonparametric tests of independence”, J. Machine Learning Research, 11 (2010), 1391–1423 | MR | Zbl

[12] Heller R., Heller Y., Gorfine M., A consistent multivariate test of association based on ranks of distances, 2012, arXiv: math/1201.3522v3 | MR

[13] Heller R., Gorfine M., Heller Y., “A class of multivariate distribution-free tests of independence based on graphs”, J. Statist. Plan. Inference, 142:12 (2012), 3097–3106 | DOI | MR | Zbl

[14] Hoffman R., Jain A., “A test of randomness based on the minimal spanning tree”, Patt. Recogn. Lett., 1983, 175–180 | DOI

[15] Pan G., Gao J., Yang Y., Guo M., Independence test for high dimensional random vectors, 2012, arXiv: math.ST/1205.6607

[16] Petrie A., Willemain T/R/, “An empirical study of tests for uniformity in multidimensional data”, Computat. Statist. Data Anal., 64 (2013), 253–268 | DOI | MR | Zbl

[17] Roy A., Ghosh A.K., “Some tests of independence based on maximum mean discrepancy and ranks of nearest neighbors”, Statist. and Probab. Letters, 164 (2020), 108793 | DOI | MR | Zbl

[18] Steele J., “Growth rates of Euclidean minimal spanning trees with power-weighted edges”, Ann. Probab., 16 (1988), 1767–1787 | DOI | MR | Zbl

[19] Székely G.J., Rizzo M.L., “Energy statistics: A class of statistics based on distances”, J. Statist. Plann. Inference, 143 (2013), 1249–1272 | DOI | MR

[20] Tenreiro C., “On the finite sample behavior of fixed bandwidth Bickel–Rosenblatt test for univariate and multivariate uniformity”, Commun. Statist. Simul. and Comput., 36 (2007), 827–846 | DOI | MR | Zbl

[21] Yang M., Modarres R., “Multivariate tests of uniformity”, Stat. Papers, 58:3 (2017), 627–639 | DOI | MR | Zbl