Conditional tests for elliptical symmetry using robust estimators

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

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 4, 1744-1765

Abstract: 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. Under mild assumptions that include elliptical distributions without first moments, we derive the test statistic asymptotic behavior under the null hypothesis and under special alternatives. Numerical experiments allow to compare the behavior 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.

Date: 2017
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DOI: 10.1080/03610926.2015.1026997

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