133
Views
0
CrossRef citations to date
0
Altmetric
Articles

Testing bivariate symmetry

ORCID Icon &
Pages 477-502 | Received 27 Apr 2022, Accepted 05 Jun 2023, Published online: 14 Jun 2023

References

  • Bell, C.B., and Haller, H.S. (1969), ‘Bivariate Symmetry Tests: Parametric and Nonparametric’, The Annals of Mathematical Statistics, 40, 259–269. https://doi.org/10.1214/aoms/1177697821
  • Boshnakov, G.N. (2007), ‘Some Measures for Asymmetry of Distributions’, Statistics & Probability Letters, 77, 1111–1116. http://www.sciencedirect.com/science/article/pii/S0167715207000624
  • Chacón, J.E., and Duong, T. (2018), Multivariate Kernel Smoothing and Its Applications. Monographs on Statistics and Applied Probability, Vol. 160, Boca Raton, FL: CRC Press. https://doi.org/10.1201/9780429485572
  • Critchley, F., and Jones, M.C. (2008), ‘Asymmetry and Gradient Asymmetry Functions: Density-Based Skewness and Kurtosis’, Scandinavian Journal of Statistics, 35, 415–437. https://doi.org/10.1111/j.1467-9469.2008.00599.x
  • Dai, X., Niu, C., and Guo, X. (2018), ‘Testing for Central Symmetry and Inference of the Unknown Center’, Computational Statistics & Data Analysis, 127, 15–31. https://doi.org/10.1016/j.csda.2018.05.007
  • Einmahl, J.H.J., and Gan, Z. (2016), ‘Testing for Central Symmetry’, Journal of Statistical Planning and Inference, 169, 27–33. https://doi.org/10.1016/j.jspi.2015.07.006
  • Fleming, T.R., and Harrington, D.P. (1991), Counting Processes and Survival Analysis, Hoboken, NJ: John Wiley & Sons.
  • Frees, E.W., and Valdez, E.A. (1998), ‘Understanding Relationships Using Copulas’, North American Actuarial Journal, 2, 1–25. https://doi.org/10.1080/10920277.1998.10595667
  • Gens, R., and Domingos, P. (2014), ‘Deep Symmetry Networks’, in Proceedings of the 27th International Conference on Neural Information Processing Systems – Volume 2, NIPS'14, Cambridge, MA, USA: MIT Press, pp. 2537–2545, http://dl.acm.org/citation.cfm?id=2969033.2969110.
  • Hall, P., and Marron, J.S. (1987), ‘Estimation of Integrated Squared Density Derivatives’, Statistics & Probability Letters, 6, 109–115. https://doi.org/10.1016/0167-7152(87)90083-6
  • Heathcote, C., Rachev, S., and Cheng, B. (1995), ‘Testing Multivariate Symmetry’, Journal of Multivariate Analysis, 54, 91–112. http://www.sciencedirect.com/science/article/pii/S0047259X85710469
  • Hollander, M. (1971), ‘A Nonparametric Test for Bivariate Symmetry’, Biometrika, 58, 203–212. http://www.jstor.org/stable/2334332
  • Jaser, M., and Min, A. (2021), ‘On Tests for Symmetry and Radial Symmetry of Bivariate Copulas Towards Testing for Ellipticity’, Computational Statistics, 36, 1–26.
  • Kasuya, E. (2010), ‘Wilcoxon Signed-Ranks Test: Symmetry Should Be Confirmed Before the Test’, Animal Behaviour, 79, 765–767.
  • Koldanov, P., and Lozgacheva, N. (2016), ‘Multiple Testing of Sign Symmetry for Stock Return Distributions’, International Journal of Theoretical and Applied Finance, 19, 1650049. https://doi.org/10.1142/S0219024916500497
  • Laska, E., Meisner, M., and Wanderling, J. (2014), ‘Exact Distribution of a Maximally Selected Wilcoxon and a New Hybrid Test of Symmetry’, Statistics in Medicine, 33, 4292–4305. https://doi.org/10.1002/sim.6234
  • Li, X., and Morris, J.M. (1991), ‘On Measuring Asymmetry and the Reliability of the Skewness Measure’, Statistics & Probability Letters, 12, 267–271. https://ideas.repec.org/a/eee/stapro/v12y1991i3p267-271.html
  • Lyubchich, V., Wang, X., Heyes, A., and Gel, Y.R. (2016), ‘A Distribution-free m-out-of-n Bootstrap Approach to Testing Symmetry About An Unknown Median’, Computational Statistics & Data Analysis, 104, 1–9. https://doi.org/10.1016/j.csda.2016.05.004
  • Mandrekar, S.J., and Mandrekar, J.N. (2003), ‘Are Our Data Symmetric?’, Statistical Methods in Medical Research, 12, 505–513.
  • Nelsen, R.B. (1993), ‘Some Concepts of Bivariate Symmetry’, Journal of Nonparametric Statistics, 3, 95–101. https://doi.org/10.1080/10485259308832574
  • Patil, P.N., Bagkavos, D., and Wood, A.T. (2014), ‘A Measure of Asymmetry Based on a New Necessary and Sufficient Condition for Symmetry’, Sankhya A, 76, 123–145. https://doi.org/10.1007/s13171-013-0034-Z
  • Patil, P.N., Patil, P.P., and Bagkavos, D. (2012), ‘A Measure of Asymmetry’, Statistical Papers, 53, 971–985. https://doi.org/10.1007/s00362-011-0401-6
  • Rao, K.S.M., and Raghunath, M. (2012), ‘A Simple Nonparametric Test for Bivariate Symmetry About a Line’, Journal of Statistical Planning and Inference, 142, 430–444. https://doi.org/10.1016/j.jspi.2011.07.025
  • Riahi, S., and Patil, P.N. (2021), ‘Testing for Central Symmetry and Symmetry About An Axis’, Communications in Statistics – Simulation and Computation, 52, 717–734. https://doi.org/10.1080/03610918.2020.1866204.
  • Serfling, R.J. (1980), Approximation Theorems of Mathematical Statistics. Wiley Series in Probability and Mathematical Statistics, New York: John Wiley & Sons, Inc..
  • Silverman, B.W. (1986), Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability, London: Chapman & Hall. https://doi.org/10.1007/978-1-4899-3324-9
  • Su, L. (2006), ‘A Simple Test for Multivariate Conditional Symmetry’, Economics Letters, 93, 374–378. https://doi.org/10.1016/j.econlet.2006.06.013
  • Wand, M.P., and Jones, M.C. (1994), Kernel Smoothing. Chapman & Hall/CRC Monographs on Statistics & Applied Probability, Vol. 60, Boca Raton, FL, U.S.: Chapman & Hall. http://oro.open.ac.uk/28198/
  • Zwet, W.R.V. (1964), Convex Transformations of Random Variables, Mathematical Centre Tracts (Vol. 7), Amsterdam: Mathematisch Centrum.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.