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Original Articles

Conditional tests for elliptical symmetry using robust estimators

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Pages 1744-1765 | Received 14 Feb 2014, Accepted 02 Mar 2015, Published online: 10 Mar 2016

References

  • Anderson, T.W., Fang, K.T., Hsu, H. (1986). Maximum-likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions. Can. J. Stat. 14:55–59.
  • Baringhaus, L. (1991). Testing for spherical symmetry of a multivariate distribution. Ann. Stat. 19:899–917.
  • Batsidis, A., Zografos, K. (2013). A necessary test of fit of specific elliptical distributions based on an estimator of Song’s measure. J. Multivariate Anal. 113:91–105.
  • Batsidis, A., Martin, N., Pardo, L., Zografos, K. (2014). A necessary power divergence-type family of tests for testing elliptical symmetry. J. Stat. Comput. Sim. 84:57–83.
  • Beran, R. (1979). Testing for elliptical symmetry of a multivariate density. Ann. Stat. 7:150–162.
  • Bianco, A.M., Boente, G., Rodrigues, I.M. (2015). Conditional tests for elliptical symmetry using robust estimators. http://arxiv.org/abs/1502.05600
  • Ghosh, S., Ruymgaart, F.H. (1992). Applications of empirical characteristic functions in some multivariate problem. Can. J. Stat. 20:429–440.
  • Fang, K.T., Anderson, T.W., eds. (1990). Statistical Inference in Elliptically Contoured and Related Distributions. New York: Allerton Press.
  • Fang, K.T., Kotz, S., Ng, K.W. (1990). Symmetric multivariate and related distributions. In: Monographs on Statistics and Applied Probability, vol. 36. London: Chapman and Hall.
  • Fang, K.T., Zhu, L.X., Bentler, P.M. (1993). A necessary test for sphericity of a high-dimensional distribution. J. Multivariate Anal. 44:34–55.
  • Fernholz, L. (1983). Von Mises Calculus for Statistical Functionals. Lecture Notes in Statistics, vol. 19. New York: Springer Verlag.
  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A. (1986). Robust Statistics: The Approach Based on Influence Functions. New York: Wiley.
  • Huffer, F., Park, C. (2007). A test for elliptical symmetry. J. Multivariate Anal. 98:256–281.
  • Koltchinskii, V., Li, L. (1998). Testing for spherical symmetry of a multivariate distribution. J. Multivariate Anal. 65:228–244.
  • Koltchinskii, V., Sakhanenko, L. (2000). Testing for ellipsoidal symmetry of a multivariate distribution. In: Giné, E., Mason, D., Wellner, J., eds. High Dimensional Probability II (pp. 493–510). Boston: Birkhauser.
  • Lopuhaä, H. (1989). On the relation between S-estimators and M-estimators of multivariate location and covariance. Ann. Stat. 17:1662–1683.
  • Manzotti, A., Pérez, F., Quiroz, A. (2002). A test for testing the null hypothesis of elliptical symmetry. Journal of Multivariate Analysis 81:274–285.
  • Morales, D., Pardo, L., Pardo, M.C., Vajda, I. (2004). Rényi statistics for testing composite hypotheses in general exponential models. Statistics 38:133–147.
  • Muirhead, R.J. (1982). Aspects of Multivariate Statistical Theory. Canada: John Wiley & Sons.
  • Schott, J.R. (2002). Testing for elliptical symmetry in covariance-matrix-based analyses. Stat. Probab. Lett. 60:395–404.
  • Tyler, D. (1982). Radial estimates and the test for sphericity. Biometrika 69:429–436.
  • Ushakov, N.G. (1999). Selected Topics in Characteristic Functions. Series: Modern Probability and Statistics. Utrech: Walter de Gruyter.
  • van de Geer, S. (2000). Empirical Processes in M-Estimation. Cambridge: Cambridge University Press.
  • Zhu, L.-X., Neuhaus, G. (2003). Conditional tests for elliptical symmetry. J. Multivariate Anal. 84:284–298.

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