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Conditional tests for elliptical symmetry using robust estimators

Bianco, Ana M.; Boente, Graciela; Rodrigues, Isabel M.

Communications in Statistics - Theory and Methods, 46 (2017), 1744-1765

This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. We derive the asymptotic behaviour of the test statistic under the null hypothesis and under contiguous alternatives without any moment requirements on the elliptical distribution. Numerical experiments allow to compare the behaviour of the tests based on the sample mean and covariance matrix with that based on robust estimators, under various elliptical distributions and different alternatives. We also provide a numerical comparison with other competing tests.