Some count-based nonparametric tests for circular symmetry of a bivariate distribution

References

• Aki, S. 1993. On nonparametric tests for symmetry in Rm. Annals of the Institute of Statistical Mathematics 45:787–800. doi:10.1007/BF00774788.
   Google Scholar
• Al-Shiha, A. A. 2007. Bivariate symmetry and a simple generalization of the sign test for testing spherical symmetry of a bivariate distribution. Third Saudi Science Conference, Riyadh, March 10–13, 2007.
   Google Scholar
• Al-Shiha, A. A. 2009. Bivariate symmetry and a simple generalization of the sign test for testing spherical symmetry of a bivariate distribution. Journal of King Saudi University (Science Section) 21:227–32.
   Google Scholar
• Arcones, M. A., and E. Gine. 1991. Some bootstrap tests of symmetry for univariate continuous distributions. Annals of Statistics 15:1496–511. doi:10.1214/aos/1176348258.
   Google Scholar
• Baringhaus, L. 1991. Testing for spherical symmetry of a multivariate distribution. Annals of Statistics 19:899–917. doi:10.1214/aos/1176348127.
   Google Scholar
• Cabana, A., and E. M. Cabana. 2000. Tests of symmetry based on transformed empirical processes. The Canadian Journal of Statistics/La Revue Canadienne de Statistique 28:829–39. doi:10.2307/3315919.
   Google Scholar
• Chmielewski, M. A. 1981. Elliptically symmetric distributions: A review and bibliography. International Statistical Review 49:67–74. doi:10.2307/1403038.
   Google Scholar
• Csorgo, S., and C. R. Heathcote. 1987. Testing for symmetry. Biometrika 74:177–86. doi:10.1093/biomet/74.1.177.
   Google Scholar
• Diks, C., and H. Tong. 1999. A test for symmetries of multivariate probability distributions. Biometrika 86:605–14. doi:10.1093/biomet/86.3.605.
   Google Scholar
• Duong, T. 2007. ks: Kernel density estimation and kernel discriminant analysis for multivariate data in R. Journal of Statistical Software 21 (7):1–16. doi:10.18637/jss.v021.i07.
   Google Scholar
• Einmahl, J. H. J., and M. Gantner. 2012. Testing for bivariate spherical symmetry. Test 21:54–73. doi:10.1007/s11749-011-0235-5.
   Google Scholar
• Feller, W. 2005. An introduction to probability theory and its applications, vol. I, 3rd ed. New York: Wiley.
   Google Scholar
• Gupta, M. K. 1967. An asymptotically nonparametric test of symmetry. Annals of Mathematical Statistics 38:889–96.
   Google Scholar
• Heatcote, C. R., S. T. Rachev, and B. Cheng. 1995. Testing multivariate symmetry. Journal of Multivariate Analysis 54:91–112. doi:10.1006/jmva.1995.1046.
   Google Scholar
• Hollander, M., and D. A. Wolfe. 1999. Nonparametric statistical methods. New York: Wiley.
   Google Scholar
• Koltchinskii, V. I., and L. Li. 1998. Testing for spherical symmetry of a multivariate distribution. Journal of Multivariate Analysis 65:228–44. doi:10.1006/jmva.1998.1743.
   Google Scholar
• Liang, J., K.-T. Fang, and F. J. Hickernell. 2008. Some necessary uniform tests for spherical symmetry. Annals of the Institute of Statistical Mathematics 60:679–96.
   Google Scholar
• Liu, R. Y., J. M. Parelius, and K. Singh, 1999. Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion). Annals of Statistics 27:783–858. doi:10.1214/aos/1018031259.
   Google Scholar
• Madhava Rao, K. S., and M. Raghunath. 2012. A simple nonparametric test for bivariate symmetry about a line. Journal of Statistical Planning and Inference 142:430–44. doi:10.1016/j.jspi.2011.07.025.
   Google Scholar
• Nelsen, R. B. 1993. Some concepts of bivariate symmetry. Journal of Nonparametric Statistics 3:95–101. doi:10.1080/10485259308832574.
   Google Scholar
• Randles, H., M. A. Fligner, G. E. Polisectoro, and D. A. Wolfe. 1980. An asymptotically distribution-free test for symmetry versus asymmetry. Journal of American Statistical Association 75:168–72.
   Google Scholar
• Rothman, E. D., and M. Woodroofe. 1972. A Cramer–von Mises statistic for testing symmetry. Annals of Mathematical Statistics 43:2035–38. doi:10.1214/aoms/1177690879.
   Google Scholar
• Schuster, E. F., and R. C. Barker. 1987. Using the bootstrap in testing symmetry versus asymmetry. Communications in Statistics—Simulation and Computation 16:69–84. doi:10.1080/03610918708812578.
   Google Scholar
• Serfling, R. J. (2006) Multivariate symmetry and asymmetry. In Encyclopaedia of statistical sciences, ed. S. Kotz, N. Balakrishnan, C. B. Read, and B. Vidakovic, vol. 8, 2nd ed., 5338–5345. New York: Wiley.
   Google Scholar
• Smith, P. J. 1977. A nonparametric test for bivariate circular symmetry based on the empirical cdf. Communications in Statistics—Theory and Methods 6:209–20. doi:10.1080/03610927708827484.
   Google Scholar
• Vexler, A., A. D. Hutson, and X. Chen. 2016. Statistical testing strategies in the health sciences. New York: Chapman & Hall/CRC.
   Google Scholar