A necessary power divergence-type family of tests for testing elliptical symmetry

Abstract

This 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.