Testing for spherical and elliptical symmetry
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Date
2020-11
Publication Type
Journal Article
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Abstract
We construct new testing procedures for spherical and elliptical symmetry based on the characterization that a random vector X with finite mean has a spherical distribution if and only if E[u⊤X|v⊤X]=0 holds for any two perpendicular vectors u and v. Our test is based on the Kolmogorov–Smirnov statistic, and its rejection region is found via the spherically symmetric bootstrap. We show the consistency of the spherically symmetric bootstrap test using a general Donsker theorem which is of some independent interest. For the case of testing for elliptical symmetry, the Kolmogorov–Smirnov statistic has an asymptotic drift term due to the estimated location and scale parameters. Therefore, an additional standardization is required in the bootstrap procedure. In a simulation study, the size and the power properties of our tests are assessed for several distributions and the performance is compared to that of several competing procedures. © 2020 Elsevier Inc.
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published
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Journal / series
Volume
180
Pages / Article No.
104667
Publisher
Elsevier
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Software
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Subject
Bootstrap; Elliptical symmetry; Empirical process; Kolmogorov–Smirnov test; Spherical symmetry
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08845 - Balabdaoui, Fadoua (Tit.-Prof.) / Balabdaoui, Fadoua (Tit.-Prof.)