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AbstractThis paper presents a family of power divergence-type test statistics for testing the hypothesis of elliptical symmetry. We assess the performance of the new family of test statistics, using Monte Carlo simulation. In this context, the type I error rate as well as the power of the tests are studied. Specifically, for selected alternatives, we compare the power of the proposed procedure with that proposed by Schott Testing for elliptical symmetry in covariance-matrix-based analyses, Stat. Probab. Lett. 60 (2002), pp. 395–404. This last test statistic is an easily computed one with a tractable null distribution and very good power for various alternatives, as it has established in previous published simulations studies F. Huffer and C. Park, A test for elliptical symmetry, J. Multivariate Anal. 98 (2007), pp. 256–281; L. Sakhanenko, Testing for ellipsoidal symmetry: A comparison study, Comput. Stat. Data Anal. 53 (2008), pp. 565–581. Finally, a well-known real data set is used to illustrate the method developed in this paper.Keywords: elliptical symmetryspherical symmetrypower divergenceMonte Carlo study AcknowledgementsWe thank the anonymous referee for his/her valuable comments and suggestions which greatly improved the paper, which was partially supported by Grant MTM 2009-10072.
Batsidis et al. (Thu,) studied this question.
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