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- W4285687551 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 $Ex[u^top X | v^top X] = 0$ 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." @default.
- W4285687551 created "2022-07-17" @default.
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- W4285687551 date "2020-04-27" @default.
- W4285687551 modified "2023-09-25" @default.
- W4285687551 title "Testing for spherical and elliptical symmetry" @default.
- W4285687551 doi "https://doi.org/10.48550/arxiv.2004.13151" @default.
- W4285687551 hasPublicationYear "2020" @default.
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