Permutation tests of multivariate location using data depth

References

• Hotelling H. The generalization of Student's ratio. Ann Math Stat. 1931;2(3):360–378. doi: 10.1214/aoms/1177732979
   Google Scholar
• Hodges JL. A bivariate sign test. Ann Math Stat. 1955;26(3):523–527. doi: 10.1214/aoms/1177728498
   Google Scholar
• Blumen I. A new bivariate sign test. J Am Stat Assoc. 1958;53(282):448–456. doi: 10.1080/01621459.1958.10501451
   Web of Science ®Google Scholar
• Oja H, Nyblom J. Bivariate sign tests. J Am Stat Assoc. 1989;84(405):249–259. doi: 10.1080/01621459.1989.10478763
   Web of Science ®Google Scholar
• Oja H. Descriptive statistics for multivariate distributions. Stat Probab Lett. 1983;1(6):327–332. doi: 10.1016/0167-7152(83)90054-8
   Google Scholar
• Brown BM, Hettmansperger TP. Affine invariant rank methods in the bivariate location model. J R Stat Soc Ser B (Methodol). 1987;49(3):301–310.
   Google Scholar
• Brown BM, Hettmansperger TP. An affine invariant bivariate version of the sign test. J R Stat Soc Ser B (Methodol). 1989;51(1):117–125.
   Google Scholar
• Randles RH. A distribution-free multivariate sign test based on interdirections. J Am Stat Assoc. 1989;84:1045–1050. doi: 10.1080/01621459.1989.10478870
   Web of Science ®Google Scholar
• Peters D, Randles RH. A multivariate signed-rank test for the one-sample location problem. J Am Stat Assoc. 1990;85:552–557. doi: 10.1080/01621459.1990.10476234
   Web of Science ®Google Scholar
• Liu RY. on a notion of data depth based on random simplices. Ann Stat. 1990;18:405–414. doi: 10.1214/aos/1176347507
   Web of Science ®Google Scholar
• Serfling RJ, Wang Y. On Liu's simplicial depth and Randles' interdirections. Comput Stat Data Anal. 2016;99:235–247. doi: 10.1016/j.csda.2016.02.002
   Web of Science ®Google Scholar
• Blair RC, Higgins JJ, Karniski W, et al. A study of multivariate permutation tests which may replace Hotelling's T2 test in prescribed circumstances. Multivariate Behav Res. 1994;29(2):141–163. doi: 10.1207/s15327906mbr2902_2
   PubMed Web of Science ®Google Scholar
• Holmes AP, Blair RC, Watson JD, et al. Nonparametric analysis of statistic images from functional mapping experiments. J Cereb Blood Flow Metab. 1996;16(1):7–22. doi: 10.1097/00004647-199601000-00002
   PubMed Web of Science ®Google Scholar
• Nichols TE, Holmes AP. Nonparametric permutation tests for functional neuroimaging: a primer with examples. Hum Brain Mapp. 2002;15(1):1–25. doi: 10.1002/hbm.v15:1
   PubMed Web of Science ®Google Scholar
• Helwig NE. Robust nonparametric tests of general linear model coefficients: a comparison of permutation methods and test statistics. NeuroImage. 2019;201:116030. doi: 10.1016/j.neuroimage.2019.116030
   PubMed Web of Science ®Google Scholar
• Möttönen J, Oja H. Multivariate spatial sign and rank methods. J Nonparametr Stat. 1995;5:201–213. doi: 10.1080/10485259508832643
   Google Scholar
• Hettmansperger TP, Nyblom J, Oja H. Affine invariant multivariate one-sample sign tests. J R Stat Soc Ser B (Methodol). 1994;56(1):221–234.
   Google Scholar
• Hettmansperger TP, Mottonen J, Oja H. Affine-invariant multivariate one-sample signed-rank tests. J Am Stat Assoc. 1997;92(440):1591–1600. doi: 10.1080/01621459.1997.10473681
   Web of Science ®Google Scholar
• Randles RH. A simpler, affine-invariant, multivariate, distribution-free sign test. J Am Stat Assoc. 2000;95:1263–1268. doi: 10.1080/01621459.2000.10474326
   Web of Science ®Google Scholar
• Tyler DE. A distribution-free M-estimator of multivariate scatter. Ann Stat. 1987;15(1):234–251. doi: 10.1214/aos/1176350263
   Web of Science ®Google Scholar
• Hallin M, Paindaveine D. Optimal tests for multivariate location based on interdirections and pesudo-Mahalanobis ranks. Ann Math Stat. 2002;30:1103–1133.
   Google Scholar
• Hallin M, Paindaveine D. Multivariate Signed Ranks: Randles' Interdirections or Tyler's Angles. In: Statistical data analysis based on the L1-norm and related methods. Birkhuser, Basel; 2002: p. 271–282.
   Google Scholar
• Mahfoud ZR, Randles RH. On multivariate signed-rank tests. J Nonparametr Stat. 2005;17:201–216. doi: 10.1080/1048525042000267806
   Web of Science ®Google Scholar
• Dehghan S, Faridrohani MR. Affine invariant depth-based tests for the multivariate one-sample location problem. Test. 2019;28(3):671–693. doi: 10.1007/s11749-018-0593-3
   Web of Science ®Google Scholar
• Dehghan S, Faridrohani MR. Nonparametric depth-based tests for the multivariate location problem. Aust N Z J Stat. 2021;63(2):309–330. doi: 10.1111/anzs.v63.2
   Web of Science ®Google Scholar
• Dehghan S, Faridrohani MR, Barzegar Z. Testing for diagonal symmetry based on center-outward ranking. Stat Pap. 2023;64:255–283. doi: 10.1007/s00362-022-01316-w
   Web of Science ®Google Scholar
• Liu RY, Singh K. A quality index based on data depth and multivariate rank tests. J Am Stat Assoc. 1993;88(421):252–260.
   Web of Science ®Google Scholar
• Li J, Liu RY. New nonparametric tests of multivariate locations and scales using data depth. Stat Sci. 2004;19(4):686–696. doi: 10.1214/088342304000000594
   Web of Science ®Google Scholar
• Liu RY, Singh K. Rank tests for multivariate scale difference based on data depth. DIMACS Ser Discrete Math Theoret Comput Sci. 2006;72:17–35. doi: 10.1090/dimacs/072
   Google Scholar
• Barale MS, Shirke DT. A test based on data depth for testing location-scale of the two multivariate populations. J Stat Comput Simul. 2021;91(4):768–785. doi: 10.1080/00949655.2020.1830285
   Web of Science ®Google Scholar
• Liu Z, Modarres R, Yang M. A multivariate control quantile test using data depth. Comput Stat Data Anal. 2013;57(1):262–270. doi: 10.1016/j.csda.2012.06.013
   Web of Science ®Google Scholar
• Dyckerhoff R, Ley C, Paindaveine D. Depth-based runs tests for bivariate central symmetry. Ann Inst Stat Math. 2015;67(5):917–941. doi: 10.1007/s10463-014-0480-y
   Web of Science ®Google Scholar
• Dehghan S, Faridrohani MR. Depth-based signed-rank tests for bivariate central symmetry. REVSTAT-Stat J. 2020;18(1):109–129.
   Web of Science ®Google Scholar
• Pawar SD, Shirke DT. Nonparametric tests for multivariate multi-sample locations based on data depth. J Stat Comput Simul. 2019;89(9):1574–1591. doi: 10.1080/00949655.2019.1590577
   Web of Science ®Google Scholar
• Shirke DT, Chavan AR. Multivariate multi-sample tests for location based on data depth. J Stat Comput Simul. 2019;89(18):3377–3390. doi: 10.1080/00949655.2019.1667359
   Web of Science ®Google Scholar
• Dehghan S, Faridrohani MR. Multivariate tests for the multisample location problem based on depth function. Stat. 2022;11(1):e423. doi: 10.1002/sta4.v11.1
   Web of Science ®Google Scholar
• Singh R, Dutta S, Misra N. Some multivariate goodness of fit tests based on data depth. J Nonparametr Stat. 2022;34(2):428–447. doi: 10.1080/10485252.2022.2064998
   Web of Science ®Google Scholar
• Zuo Y, Serfling RJ. General notions of statistical depth function. Ann Stat. 2000a;28(2):461–482.
   Web of Science ®Google Scholar
• Tukey J. Mathematics and picturing of data. In: Proceeding of the International congress of Mathematicians; 1975.
   Google Scholar
• Liu RY. On a notion of simplicial depth. Proc Nati Acad Sci. 1988;85(6):1732–1734. doi: 10.1073/pnas.85.6.1732
   PubMed Web of Science ®Google Scholar
• Liu RY. Data depth and multivariate rank tests. In: Dodge Y, editor. L1-Statistical Analysis and Related Methods. 1992. p. 279–294.
   Google Scholar
• Zuo Y. Projection-based depth functions and associated medians. Ann Stat. 2003;31(5):1460–1490. doi: 10.1214/aos/1065705115
   Web of Science ®Google Scholar
• Chaudhuri P. On a geometric notion of quantiles for multivariate data. J Am Stat Assoc. 1996;91(434):862–872. doi: 10.1080/01621459.1996.10476954
   Web of Science ®Google Scholar
• Mosler K, Mozharovskyi P. Choosing among notions of multivariate depth statistics. Stat Sci. 2022;37(3):348–368. doi: 10.1214/21-STS827
   Web of Science ®Google Scholar
• Sleasman JW, Nelson RP, Goodenow MM, et al. Immunoreconstitution after ritonavir therapy in children with human immunodeficiency virus infection involves multiple lymphocyte lineages. J Pediatr. 1999;134(5):597–606. doi: 10.1016/S0022-3476(99)70247-7
   PubMed Web of Science ®Google Scholar
• Larocque D, Labarre M. A conditionally distribution-free multivariate sign test for one-sided alternatives. J Am Stat Assoc. 2004;99(466):499–509. doi: 10.1198/016214504000000485
   Web of Science ®Google Scholar