85
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

On some validity-robust tests for the homogeneity of concentrations on spheres

Pages 372-383 | Received 23 Sep 2014, Accepted 10 Mar 2015, Published online: 14 May 2015

References

  • Fisher, N.I. (1982), ‘Robust Estimation of the Concentration Parameter of Fisher's Distribution on the Sphere’, Journal of the Royal Statistical Society Series C, 31, 152–154.
  • Hájek, J., and Šidák, Z. (1967), ‘Theory of Rank Tests. New York: Academic Press.
  • Kato, S., and Jones, M.C. (2010), ‘A Family of Distributions on the Circle with Links to, and Applications Arising from, Möbius Transformation’, Journal of the American Statistical Association, 102, 249–262. doi: 10.1198/jasa.2009.tm08313
  • Ko, D. (1992), ‘Robust Estimation of the Concentration Parameter of the von Mises–Fisher Distribution’, Annals of Statistics, 20, 917–928. doi: 10.1214/aos/1176348663
  • Ko, D., and Guttorp, P. (1988), ‘Robustness of Estimators for Directional Data’, Annals of Statistics, 16, 609–618. doi: 10.1214/aos/1176350822
  • Kreiss J.-P. (1987), ‘On Adaptive Estimation in Stationary ARMA Processes’, Annals of Statistics, 15, 112–133. doi: 10.1214/aos/1176350256
  • Kruskal, W.H., and Wallis, W.A. (1952), ‘Use of Ranks in One-Criterion Variance Analysis’, Journal of the American Statistical Association, 47(260), 583–621. doi: 10.1080/01621459.1952.10483441
  • Larsen, P.V., Blæsild, P., and Sørensen, M.K. (2002), ‘Improved Likelihood Ratio Tests on the von Mises–Fisher Distribution’, Biometrika, 89, 947–951. doi: 10.1093/biomet/89.4.947
  • Ley, C., Swan, Y., Thiam, B., and Verdebout, T. (2013), ‘Optimal R-Estimation of a Spherical Location’, Statistica Sinica, 23, 305–332.
  • Ley, C., and Verdebout, T. (2014), ‘Local Powers of Optimal One- and Multi-Sample Tests for the Concentration of Fisher–von Mises–Langevin Distributions’, International Statistical Review, 82, 440–456. doi: 10.1111/insr.12047
  • Mardia, K.V., and Jupp, P.E. (2000), ‘Directional Statistics. New York: Wiley.
  • Paindaveine, D., and Verdebout, T. (2015), ‘Optimal Rank-Based Tests for the Location Parameter of a Rotationally Symmetric Distribution on the Hypersphere’, in Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels, eds. M. Hallin, D. Mason, D. Pfeifer, and J. Steinebach, Springer, pp. 249–270. http://link.springer.com/chapter/10.1007%2F978-3-319-12442-1_14.
  • Stephens, M.A. (1969), ‘Multi-Sample Tests for the Fisher Distribution for Directions’, Biometrika, 56, 169–181. doi: 10.1093/biomet/56.1.169
  • Watamori, Y., and Jupp, P.E. (2005), ‘Improved Likelihood Ratio and Score Tests on Concentration Parameters of von Mises–Fisher Distributions’, Statistics and Probability Letters, 72, 93–102. doi: 10.1016/j.spl.2004.10.017
  • Watson, G.S. (1983), ‘Statistics on Spheres. New York: Wiley.
  • Watson, G.S. (1986), ‘Some Estimation Theory on the Sphere’, Annals of the Institute of Statistical Mathematics, 38, 263–275. doi: 10.1007/BF02482515

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.